tag:blogger.com,1999:blog-81253184932335571092024-03-18T16:42:20.514+07:00Everything About MathHere we can share knowledge.hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.comBlogger181125tag:blogger.com,1999:blog-8125318493233557109.post-91220680023397996642010-01-04T20:38:00.005+07:002010-01-04T21:07:20.956+07:00Magic Square yang KonsentrikLagi-lagi post mengenai Magic Square. Kali ini, soalnya lebih rumit daripada sebelumnya yang hanya 3x3.<br /><blockquote>Lihatlah Magic Square di bawah ini.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfv8UhuCoyh4B38SOzSfHyTTvgzi_IP3Itm8xkkgysAZl7pnymYvnEjqcsXG73yL63kMUL48uhLiOUVUB7mst2ZDpIbPplvf_afE29sTiLi_tIvOzP9bNYqSlOQxcvj7Uq0-cZpkThdjcW/s1600-h/consentric+5x5.JPG"><img style="cursor: pointer; width: 205px; height: 185px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfv8UhuCoyh4B38SOzSfHyTTvgzi_IP3Itm8xkkgysAZl7pnymYvnEjqcsXG73yL63kMUL48uhLiOUVUB7mst2ZDpIbPplvf_afE29sTiLi_tIvOzP9bNYqSlOQxcvj7Uq0-cZpkThdjcW/s400/consentric+5x5.JPG" alt="" id="BLOGGER_PHOTO_ID_5422880261732038562" border="0" /></a><br /></div><div style="text-align: justify;">Seperti yang telah disinggung sebelumnya tentang *concentric*. Magic Square 5x5 di atas memiliki sifat menarik bahwa persegi 3x3 di dalamnya juga merupakan magic square.<br /></div><br /><div style="text-align: justify;">Namun, sesungguhnya persegi 5x5 ini bukan satu-satunya magic square yang dapat dibentuk. <span style="background: rgb(255, 182, 6) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Bisakah kalian memperoleh susunan magic square 5x5 konsentrik lainnya?</span><br /></div></blockquote><div style="text-align: justify;">Gagasan Concentric Magic Square ini dapat diperluas. Misalnya, kita memiliki magic square 9x9 yang di dalam dirinya terdapat magic square 7x7 yang di dalam dirinya terdapat magic square 5x5 yang di dalam dirinya lagi terdapat magic square 3x3.<br /></div><blockquote><span style="background: rgb(255, 182, 6) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Cobalah sempurnakan Concentric Magic Square di bawah ini.</span> :)</blockquote><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhvMsfhuuWXGuJxp2sHKe0l6JKUauJE3STnhsCxgj3YHtg2eqZ6K3yBRQTD38Th9yDsqOFtWtBLjCpfHE4G-3Uhab2QmNg2bYfPOsMZPmMkmbSvRVNMPkipOaLGybcOMXN5WbPXPMcmJQa/s1600-h/concntric+9x9.JPG"><img style="cursor: pointer; width: 362px; height: 327px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhvMsfhuuWXGuJxp2sHKe0l6JKUauJE3STnhsCxgj3YHtg2eqZ6K3yBRQTD38Th9yDsqOFtWtBLjCpfHE4G-3Uhab2QmNg2bYfPOsMZPmMkmbSvRVNMPkipOaLGybcOMXN5WbPXPMcmJQa/s400/concntric+9x9.JPG" alt="" id="BLOGGER_PHOTO_ID_5422885079729744178" border="0" /></a><br /></div>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com78tag:blogger.com,1999:blog-8125318493233557109.post-71837682830070793042010-01-03T17:28:00.005+07:002010-01-05T22:32:16.180+07:00Mengisi Magic Square<table border="2" bordercolor="#33cccc" cellpadding="2" cellspacing="5"><tbody><tr><td><div style="text-align: justify;">Jika di <a href="http://hendrydext.blogspot.com/2010/01/mengenal-magic-square.html">post sebelumnya</a>, kita sudah membahas <span style="font-style: italic;">magic square</span> alias bujur sangkar ajaib. Di post ini, akan kita singgung lagi magic square. Pokoke ampe kalian *butek*, tapi jadi *ahli*.. hehehe. Berikut adalah teka-teki yang seringkali diajukan guru SD, atau mungkin guru SMP, namun beberapa orang kuliah seringkali kesulitan dalam menjawabnya..<br /></div><blockquote><div style="text-align: justify;">Total baris/kolom/diagonal bagi bujur sangkar ajaib dibawah ini adalah 20. Dua bilangan sudah diberikan. Cobalah cari bilangan-bilangan lainnya dan isikan ke dalam bujur sangkar ajaib ini.<br /></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd8Mpd3hM1dWMNxTJEj_iLVWl-qZj0U4Nddbv46SvbjQsV3MPtT1TIowb3lE6jxv9Rr0-z-pZ_070cXt5Z9595Cp92d7_xtqmw7zG1xKOHr15sDbt-NYjdm0bT1zJj6Qek1WoVh4YiMv0r/s1600-h/3x3.JPG"><img style="cursor: pointer; width: 145px; height: 124px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd8Mpd3hM1dWMNxTJEj_iLVWl-qZj0U4Nddbv46SvbjQsV3MPtT1TIowb3lE6jxv9Rr0-z-pZ_070cXt5Z9595Cp92d7_xtqmw7zG1xKOHr15sDbt-NYjdm0bT1zJj6Qek1WoVh4YiMv0r/s400/3x3.JPG" alt="" id="BLOGGER_PHOTO_ID_5422850764169042306" border="0" /></a></div></blockquote>HINT: lihat <a href="http://hendrydext.blogspot.com/2010/01/mengenal-magic-square.html">Mengenal Magic Square</a>.</td></tr></tbody></table><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><span style="font-weight: bold;">PENYELESAIAN</span><br /></div>Magic Square ini dapat diselesaikan dengan SPL (sistem persamaan Linear), namun seperti yang sudah dibuktikan sebelumnya bahwa kotak tengah pada magic square 3x3 selalu 1/3 dari jumlah total, artinya kotak di tengah adalah <sup>1</sup>/<sub>3</sub> * 20 = 6 <sup>2</sup>/<sub>3</sub>.<br /><br />Dengan mengetahui kotak di tengah, kita dapat dengan cepat menyelesaikan magic square ini.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0_0Yw7yhlnIzDZb39OR1Uy-gzOm8r6MAhrT8Ao0XKVFnk1JSHsVE5xUChcG0fzidFolpKSBczky_nTRkULcGaO0Xh8p6BEL0MmJo2y5VOHgJAnAUMWm0v-1oMJuSdsHbf_lYTzaWm1w76/s1600-h/fill.JPG"><img style="cursor: pointer; width: 146px; height: 125px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0_0Yw7yhlnIzDZb39OR1Uy-gzOm8r6MAhrT8Ao0XKVFnk1JSHsVE5xUChcG0fzidFolpKSBczky_nTRkULcGaO0Xh8p6BEL0MmJo2y5VOHgJAnAUMWm0v-1oMJuSdsHbf_lYTzaWm1w76/s400/fill.JPG" alt="" id="BLOGGER_PHOTO_ID_5422854747131034594" border="0" /></a><br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com23tag:blogger.com,1999:blog-8125318493233557109.post-73575334324246093062010-01-03T09:29:00.007+07:002010-01-04T19:09:46.404+07:00Mengenal Magic SquareTentunya, sebagian besar dari pembaca sudah mengenal istilah magic square.<br /><div style="text-align: justify;">Magic Square (<span style="font-style: italic;">persegi ajaib</span>) adalah suatu persegi dengan ukuran n x n petak di mana setiap baris, kolom dan diagonal memiliki jumlah yang sama.<br /></div><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbVEtuXLxkXQz2RWIgxuiNa-bIntoe6axbILx5XxLuCO8ppr1XasCTZsbvLNW7RuyvpiGC6GNcEOIAXR3iSzBUs2BxgZF6i00rxkhm6e8v5ocXfMLBymTYuRkovzy52_bbGKuZdNN0bXBD/s1600/magic+1.jpg"><img style="cursor: pointer; width: 166px; height: 131px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbVEtuXLxkXQz2RWIgxuiNa-bIntoe6axbILx5XxLuCO8ppr1XasCTZsbvLNW7RuyvpiGC6GNcEOIAXR3iSzBUs2BxgZF6i00rxkhm6e8v5ocXfMLBymTYuRkovzy52_bbGKuZdNN0bXBD/s400/magic+1.jpg" alt="" id="BLOGGER_PHOTO_ID_5409196125571315218" border="0" /></a><br /></div><br />Ingin mengenal lebih jauh tentang magic square. Silakan lihat post di bawah. :)<span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrmSfeFPHEqP_GJwy00law2yHBqyou4uA19dJN8nFwA6TQbV8ajmGo_wdd3odWj3ed1l5JvPzbduPFHk9DMMdf8hj1gl-1z_lKtPHXKxuFE-yMwikhbGEPGaTWzGB6XryHpLU8FdwfIaPz/s1600/title.JPG"><img style="cursor: pointer; width: 264px; height: 46px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrmSfeFPHEqP_GJwy00law2yHBqyou4uA19dJN8nFwA6TQbV8ajmGo_wdd3odWj3ed1l5JvPzbduPFHk9DMMdf8hj1gl-1z_lKtPHXKxuFE-yMwikhbGEPGaTWzGB6XryHpLU8FdwfIaPz/s400/title.JPG" alt="" id="BLOGGER_PHOTO_ID_5409507775670672258" border="0" /></a><br /></div><span style="font-weight: bold;">Sejarah *Sangat Singkat* Magic Square:</span><br /><div style="text-align: justify;">Persegi ajaib sudah dikenal oleh matematikawan Cina sejak 650 Sebelum Masehi. Ada kemungkinan sudah dikenal oleh matematikawan Arab sejak abad ke-7.<br /><br />Menurut literatur Cina, terdapat legenda bahwa dahulu kala terdapat bencana banjir. Raja besar Yu (禹) berusaha untuk menyalurkan air ke laut. Pada saat itu, terlihat kura-kura dengan pola aneh pada tempurung. Ini yang menjadi landasan untuk membuat suatu persegi 3x3 di mana setaip baris, kolom dan diagonalnya sama. <span id="result_box" class="long_text"><span style="background-color: rgb(255, 255, 255);" title="This pattern, in a certain way, was used by the people in controlling the river." onmouseover="this.style.backgroundColor='#ebeff9'" onmouseout="this.style.backgroundColor='#fff'">Pola ini, dengan cara tertentu, juga digunakan oleh orang-orang dalam mengendalikan sungai. </span></span><br /><br />Selanjutnya, magic square terus dipelajari dan dikembangkan di berbagai tempat.<br /></div>Selengkapnya, silakan baca di <a href="http://en.wikipedia.org/wiki/Magic_square">http://en.wikipedia.org/wiki/Magic_square</a>.<br /><br /><span style="font-weight: bold;">Beberapa istilah/kasus Magic Square yang menarik untuk diketahui:</span><br /><table border="2"><tbody><tr><td style="text-align: center;">Normal Magic Square<br /></td><td><div style="text-align: justify;">adalah persegi yang dibentuk dengan menempatkan angka 1 hingga n<sup>2</sup>. dan tidak ada bilangan yang sama.<br /></div>Contoh: magic square 3x3 yang diisi dengan angka 1 hingga 9.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjadvwLnsjqnmCaUY0XTyrH-JlPIpPoqsObhiSduzKxGIWXvKRYDbOyZaih8X23kuYBkORUzICsdvgVGNvVIHiSgSM2IVZJaiV-hr4GrsdkS5Z2eOWWga29_Ul35il_UPDefA7Zp2ZwFiRw/s1600-h/1.JPG"><img style="cursor: pointer; width: 80px; height: 78px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjadvwLnsjqnmCaUY0XTyrH-JlPIpPoqsObhiSduzKxGIWXvKRYDbOyZaih8X23kuYBkORUzICsdvgVGNvVIHiSgSM2IVZJaiV-hr4GrsdkS5Z2eOWWga29_Ul35il_UPDefA7Zp2ZwFiRw/s400/1.JPG" alt="" id="BLOGGER_PHOTO_ID_5420305969602760050" border="0" /></a><br /></div><div style="text-align: justify;">Dalam pembahasan kita, jika dikatakan hanya "magic square", maka artinya kita membicarakan "normal magic square".<br /></div></td></tr><tr><td style="text-align: center;">Semi Magic Square<br /></td><td style="text-align: justify;">Semi Magic Square hanya mengharuskan angka pada baris dan kolom berjumlah sama, namun diagonal tidak perlu sama.<br /></td></tr><tr><td style="text-align: center;">Trivia Magic Square</td><td style="text-align: justify;">Jika magic square berbentuk 1x1 atau semua angka pada petak diisi dengan angka yang sama semuanya, maka magic square itu adalah trivial.</td></tr><tr><td style="text-align: center;">Associative Magic Square</td><td><div style="text-align: justify;">adalah normal magic square di mana petak di tengahnya adalah median dari bilangan-bilangan yang diisi.<br /></div><br />Misalnya, untuk persegi 5x5 bagian tengahnya diisi dengan 13, maka disebut associative magic square.<br /></td></tr><tr><td style="text-align: center;">Pan Magic Square<br /></td><td>Adalah normal magic square yang lebih ampuh, karena selain semua kolom dan barisnya sama, penjumlahan semua diagonalnya selalu sama. (diagonal ini melewati batas persegi).<br /><br />Contoh:<br /><div style="text-align: center;"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwnQgnkcfC5cNrSgbK_NVsRyotN-N_WGnNAp0EXvxT0z32SwNK5oJkPIEZz0usiUL2dr_9ZDb5vE-4MsBdcGEUj8VffTH1QOxRcVIlzDNONPlXA2HGJ6XeHAuz53eYbTYnhZjYJj_VicOo/s800/pan+magic.JPG" alt="" id="BLOGGER_PHOTO_ID_5420305976733582706" border="0" /><br /></div><br />Tidak ada pan magic square yang dapat dibentuk dari 3x3.<br /></td></tr><tr><td style="text-align: center;">Concentric Magic Square<br /></td><td><div style="text-align: justify;">Merupakan normal Magic Square nxn dengan n adalah ganjil dan n≥5 dan setiap persegi di dalamnya juga magic square.<br /></div><br />Contoh:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGgoScduTzT_CrpqbSqtxGhonanQZa43dd1orVHqRwA0FJcM-4Ddaet07B07YkaHbiosejuRznNu2Pp6ctFrMeXiF00ISrUT1T0QYvb-AExV8yFhaEys2ndSCq4COCGuemVBcJeElDQX5R/s1600-h/concentric.JPG"><img style="cursor: pointer; width: 172px; height: 91px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGgoScduTzT_CrpqbSqtxGhonanQZa43dd1orVHqRwA0FJcM-4Ddaet07B07YkaHbiosejuRznNu2Pp6ctFrMeXiF00ISrUT1T0QYvb-AExV8yFhaEys2ndSCq4COCGuemVBcJeElDQX5R/s400/concentric.JPG" alt="" id="BLOGGER_PHOTO_ID_5420305973535355906" border="0" /></a><br /></div>Perhatikan bahwa persegi 3x3 di dalamnya juga adalah persegi ajaib dengan jumlah 39.<br /></td></tr><tr><td style="text-align: center;">Multiplicative Magic Square</td><td><div style="text-align: justify;">Jika normal magic square menggunakan operasi penjumlahan, maka multiplicative magic square menggunakan operasi perkalian. Perkalian setiap baris, kolom, dan diagonalnya adalah sama.<br /></div><br />Contoh:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgscBhuopIr3abu6uuwzdWtwtcjgRCcQV6E2GEmFolhagnAmoH9l5g2ixaYrom5Z_le5jbghUUmE50JHlPmuhDkvWMTsiZpc-n73Vb8Dux2WVYFk0Vynh2FDYvP25_GGFm1WCh2JZ1RUHe1/s1600-h/multiplicative.JPG"><img style="cursor: pointer; width: 80px; height: 105px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgscBhuopIr3abu6uuwzdWtwtcjgRCcQV6E2GEmFolhagnAmoH9l5g2ixaYrom5Z_le5jbghUUmE50JHlPmuhDkvWMTsiZpc-n73Vb8Dux2WVYFk0Vynh2FDYvP25_GGFm1WCh2JZ1RUHe1/s400/multiplicative.JPG" alt="" id="BLOGGER_PHOTO_ID_5420305986403409778" border="0" /></a><span style="color: rgb(255, 255, 255);">____</span><img style="cursor: pointer; width: 108px; height: 132px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRWCm3Lyv1B_a0wFNHf4HJWX9zRLsXEeB4NA0uoF23D822iZEWauFpqJkSu6uqsoyaa5Uv7km4dvD3tnxBA8mAhyphenhyphenjPOZ1lCbpnBXiRr_kwnytouR-G3g99oeVWznYLLGCCdd0ob224pdpQ/s400/multiplicative2.JPG" alt="" id="BLOGGER_PHOTO_ID_5420305980293613154" border="0" /><br /></div></td></tr></tbody></table><br /><span style="font-weight: bold;">Fakta-fakta singkat Magic Square:</span><br /><table border="1"><tbody><tr><td valign="top">1. </td><td><div style="text-align: justify;">Suatu magic square 3x3 yang tidak harus normal (artinya angkanya bebas, tidak perlu urut), maka angka di bagian tengahnya selalu 1/3 dari jumlah total. Bisakah kalian membuktikannya?<br /></div><br />Sebagai contoh:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiANGNOW9trLiglBSPMkRHsPkUk6Im95HY-4v-RO8cE9xMUKodN9oTYNsQDYcU5DNzpYN40KNHJ8pVG8ReWpUK-PnkFdHjn5OizIAcE4wbjU6dwD3XiIHrWCZS3zcseaj2P8cgxBPou0CZL/s1600-h/non+normal.JPG"><img style="cursor: pointer; width: 103px; height: 56px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiANGNOW9trLiglBSPMkRHsPkUk6Im95HY-4v-RO8cE9xMUKodN9oTYNsQDYcU5DNzpYN40KNHJ8pVG8ReWpUK-PnkFdHjn5OizIAcE4wbjU6dwD3XiIHrWCZS3zcseaj2P8cgxBPou0CZL/s400/non+normal.JPG" alt="" id="BLOGGER_PHOTO_ID_5420310524278871794" border="0" /></a><br /></div>Perhatikan bahwa 5 adalah 1/3 dari 15 (jumlah total per baris/kolom/diagonal).<br />Hint: <span style="color: rgb(192, 192, 192);">Misalkan dari 9 kotak, asumsikan ada kotak yang bernilai a, b, dan c</span><br /></td></tr><tr><td valign="top">2. </td><td>Suatu normal magic square<br />3x3 hanya dapat dibentuk dengan 1 cara (tidak termasuk rotasi, refleksi)<br />4x4 dalam 880 cara.<br />5x5 dalam 275305224 cara.<br />6x6 diperkirakan mencapai 1.7745×10<sup>19</sup> cara.<br /></td></tr></tbody></table><br /><span style="font-weight: bold;">Mengkontruksi Magic Square</span><br /><div style="text-align: justify;">Mengkontruksi magic square dapat dilakukan dengan komputer. Ada pula yang dilakukan secara matematis (perhitungan) manual menggunakan konsep modulo.<br /><br />Di post ini, kita tidak akan menggunakan perhitungan matematis, tapi menggunakan metode-metode yang lebih mudah dipahami dan *klasik*, yaitu <span style="background: rgb(184, 212, 255) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Siamese, Conway's LUX, Doubly Even (Lozenge) Method, dan Strachey Method</span> (metode yang paling ribet).<br /><br />Semua metode itu akan dibahas di bawah...<br /></div><hr /><div style="text-align: center;"><span style="font-weight: bold; color: rgb(255, 255, 255);"><span style="background: rgb(48, 126, 244) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span style="font-size:130%;">Siamese Method / de la Loubère Method</span></span></span><br /></div><br /><div style="text-align: justify;">Kemungkinan besar, kalian sudah pernah mendengar cara meng"konstruksi" magic square siamese ini. (Dan, ini mungkin sudah sangat basi sekali kalau dijelaskan lagi)..<br /></div><br />Lihat ilustrasi di bawah.<br /><div style="text-align: center;"><img src="http://upload.wikimedia.org/wikipedia/commons/7/77/SiameseMethod.gif" alt="" border="0" /><br /></div><div style="text-align: justify;">Metode di atas disebut juga sebagai metode Siamese. atau juga sering disebut dengan metode de la Loubère (bacanya susah..). Ingat: Metode Siamese hanya berlaku bagi <span style="background: rgb(184, 212, 255) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"> persegi ganjil</span> , misalnya 3x3, 5x5, 7x7.<br /></div><br />Langkah-langkah metode Siamese secara general adalah sebagai berikut:<br />1. Dimulai dari angka 1. Tempatkan di baris teratas, tepat di petak tengah..<br /><div style="text-align: justify;">2. Kita bergerak ke kanan atas... Jika posisinya sudah berada di paling atas, maka pindah ke paling bawah. Jika posisinya sudah berada di paling kanan, maka pindah ke paling kiri. Kalau sudah ada petak yang terisi, pindah ke petak di bawahnya.. Ulangi langkah ini sampai semua petak terisi.<br /><br />Perhatikan ilustrasi animasi di atas. Pasti jelas deh. Sebagai latihan, coba kalian buat persegi ajaib untuk 5x5 dengan metode Siamese ini. Yang sudah tahu boleh lanjut, tapi bagi yang pertama kali denger cara ini, kalian wajib dan kudu latihan.. weks. Masak maunya disuapin mlolo. ;p.<br /><br />Berikut adalah persegi ajaib 5x5 dengan Metode Siamese (silakan dicocokan dengan jawabanmu)<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPpHqLX5vWKHNSv2LLl2z_5GRg5zdQtBPs4XaoyzRg2iYfIaG3mRslEKWluX_mBkfoBEyQM3vCYFwrlGtC-zapI3rIXSQ4OPzxiPHguhWOx5W2gKwiAOHkVWz6xrS6zpYfa8Bz_JQgnvQ2/s1600-h/siamese+5x5.JPG"><img style="cursor: pointer; width: 130px; height: 129px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPpHqLX5vWKHNSv2LLl2z_5GRg5zdQtBPs4XaoyzRg2iYfIaG3mRslEKWluX_mBkfoBEyQM3vCYFwrlGtC-zapI3rIXSQ4OPzxiPHguhWOx5W2gKwiAOHkVWz6xrS6zpYfa8Bz_JQgnvQ2/s400/siamese+5x5.JPG" alt="" id="BLOGGER_PHOTO_ID_5420321450010527090" border="0" /></a><br /></div>Oit. Bagaimana kalau angka 1-nya ingin diletakkan di tempat yang berbeda? Jawabnya, ya!! Bisa. Tapi, aturannya bisa sedikit berbeda, misalnya jika angka 1 ingin diletakkan di baris kedua bagian tengah, maka jika ada kotak yang sudah ada, dia akan pindah ke 2 kotak di atasnya. (bukan turun ke bawah 1 kotak).. Sulit juga ya dijelaskan di sini, sebaiknya, lihat sumbernya langsung di wikipedia. Di sini, tidak akan dijelaskan secara mendetail mengenai hal itu.<br /><br />Fakta menarik seputar Siamese Method:<br />Siamese Method memiliki persamaan yang sangat mirip dengan <span style="background: rgb(184, 212, 255) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Pyramid Method</span>.<br />Berikut adalah gambaran Pyramid Method dalam mengkonstruksi magic square:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRm67SDhvSIowIGIVFP6V47jvSjhN72meKXMdB_MqrYS7Rj9a5XycaWoQpctZRX0sQwq5UMOTjyKWdO57jKa2-g_3myv3mt06ILBv1h5MgMCKjPcBDcCvjAJguCMcVotgFNghUClkKKifl/s1600-h/pyramid+3x3.JPG"><img style="cursor: pointer; width: 374px; height: 189px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRm67SDhvSIowIGIVFP6V47jvSjhN72meKXMdB_MqrYS7Rj9a5XycaWoQpctZRX0sQwq5UMOTjyKWdO57jKa2-g_3myv3mt06ILBv1h5MgMCKjPcBDcCvjAJguCMcVotgFNghUClkKKifl/s400/pyramid+3x3.JPG" alt="" id="BLOGGER_PHOTO_ID_5420324798435911410" border="0" /></a><br />Kontruksi 3x3 dengan Pyramid Method<br /></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHkgbysddDI6OdHERDfTOG7LUVcYiBaMvMd5zyAvibJtcJAyf9ilcMXtYhppzEySycPGTDCDFJ3Uqh4hMmRH5tt5LN5ADrLagJtPCIdMYgYBfEXPqnve1EtIBoK0y9FUhscKt1SranODGZ/s1600-h/pyramid+5x5.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHkgbysddDI6OdHERDfTOG7LUVcYiBaMvMd5zyAvibJtcJAyf9ilcMXtYhppzEySycPGTDCDFJ3Uqh4hMmRH5tt5LN5ADrLagJtPCIdMYgYBfEXPqnve1EtIBoK0y9FUhscKt1SranODGZ/s800/pyramid+5x5.JPG" alt="" id="BLOGGER_PHOTO_ID_5420324793818546722" border="0" /></a><br /></div><div style="text-align: center;">Konstruksi persegi 5x5 dengan pyramid Method<br /></div><br />Perhatikan bahwa konstruksi Pyramid dan Siamese sebenarnya serupa. Siamese perlu mengubah *starting point* untuk angka 1 jika hasilnya benar-benar ingin seperti Pyramid Method.<br /><br /><hr /><div style="text-align: center;"><span style="font-weight: bold; color: rgb(255, 255, 255);"><span style="background: rgb(48, 126, 244) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span style="font-size:130%;">Doubly Even/ Lozenge Method</span></span></span><br /></div><br /></div>Metode ini hanya berlaku persegi yang dapat dibegi 4, misalnya 4x4, 8x8 atau 12x12.<br /><br />Caranya cukup mudah, yaitu hanya menuliskan angka secara berutuan, kemudian beberapa petak direfleksikan terhadap titik pusat.<br /><br />Sebagai contoh persegi 4x4 dibentuk sbb:<br /><table align="center" border="0" width="90%"><tbody><tr><td valign="top"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUxrKHpR9jrUxiLcewbpfJsWkhxB5krwPWP3cfc6UkAgXVGTUduVcyWqMI1kxPF6kSqJ9x0FMTqd54zKlX0a3qBJTqUHHVnmrQ7YNili0sfSfWC4S2BybAK3KnvLCUQP6WPDiFhEH98ljq/s1600-h/4x4.JPG"><img style="cursor: pointer; width: 128px; height: 95px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUxrKHpR9jrUxiLcewbpfJsWkhxB5krwPWP3cfc6UkAgXVGTUduVcyWqMI1kxPF6kSqJ9x0FMTqd54zKlX0a3qBJTqUHHVnmrQ7YNili0sfSfWC4S2BybAK3KnvLCUQP6WPDiFhEH98ljq/s400/4x4.JPG" alt="" id="BLOGGER_PHOTO_ID_5422126879077819970" border="0" /></a> </td><td>Tuliskan 1 hingga 16</td></tr><tr><td valign="top"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjczClrzzcnC-fwatM8pD42Ct_HAm-aYF72_fKFbJH_W4a0mXT6gdgxbH7NmJtbBSwMheXpNd1mzbW0lH7rz7jF8kYPbTMGLnt3Lfw82OpMT_bLiwro4mYNwlCqDKNYxwlGE9173GJO3wnf/s1600-h/4x4+after.JPG"><img style="cursor: pointer; width: 126px; height: 93px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjczClrzzcnC-fwatM8pD42Ct_HAm-aYF72_fKFbJH_W4a0mXT6gdgxbH7NmJtbBSwMheXpNd1mzbW0lH7rz7jF8kYPbTMGLnt3Lfw82OpMT_bLiwro4mYNwlCqDKNYxwlGE9173GJO3wnf/s400/4x4+after.JPG" alt="" id="BLOGGER_PHOTO_ID_5422126884372195266" border="0" /></a> </td><td>Buat tanda silang seperti yang terlihat pada gambar di samping, kemudian refleksikan setiap petak tersebut.<br /><br />Perhatikan bagaimana 1, 4, 6, 7, 10, 11, 13, dan 16 bisa berpindah.<br /></td></tr></tbody></table><br />Persegi 8x8 dibentuk sbb:<br /><table align="center" border="0" width="90%"><tbody><tr></tr><tr><td valign="top"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5iaubkWOWOMQTj3N6Ax35ND9bWFd6yf60IYODOPeFFMyLRwN5iqJmnZDjA39jrC4vCg6lV-C6A74ESB6TOUZpvzkxMewrzKLW7Aehhc7bCfEOxhg6fN4fQcTqH_Xvj1_b97fkR0aiQxBA/s1600-h/8x8.JPG"><img style="cursor: pointer; width: 243px; height: 181px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5iaubkWOWOMQTj3N6Ax35ND9bWFd6yf60IYODOPeFFMyLRwN5iqJmnZDjA39jrC4vCg6lV-C6A74ESB6TOUZpvzkxMewrzKLW7Aehhc7bCfEOxhg6fN4fQcTqH_Xvj1_b97fkR0aiQxBA/s400/8x8.JPG" alt="" id="BLOGGER_PHOTO_ID_5422130462651495138" border="0" /></a> </td><td style="text-align: center;"> Tuliskan 1 hingga 64 dan berurut.<br /></td></tr><tr><td valign="top"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoYoJzgjtN8xpMFHNLYwrB3BAEV7BGxqZ-LLPRpQL-ooCvDJX6qqMcaSzi9ePsqBIRHmZXb-c4_yQUEItaN9X5xI83zV3PcyD9wRnlWhETlcinBSLxyc3AtTJsAH1sz_kIXgGKHHV_DrZh/s1600-h/8x8.JPG"><img style="cursor: pointer; width: 245px; height: 181px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoYoJzgjtN8xpMFHNLYwrB3BAEV7BGxqZ-LLPRpQL-ooCvDJX6qqMcaSzi9ePsqBIRHmZXb-c4_yQUEItaN9X5xI83zV3PcyD9wRnlWhETlcinBSLxyc3AtTJsAH1sz_kIXgGKHHV_DrZh/s400/8x8.JPG" alt="" id="BLOGGER_PHOTO_ID_5422338785317554722" border="0" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5iaubkWOWOMQTj3N6Ax35ND9bWFd6yf60IYODOPeFFMyLRwN5iqJmnZDjA39jrC4vCg6lV-C6A74ESB6TOUZpvzkxMewrzKLW7Aehhc7bCfEOxhg6fN4fQcTqH_Xvj1_b97fkR0aiQxBA/s1600-h/8x8.JPG"><br /></a> </td><td>Buat tanda silang yang terbagi menjadi 4 bagian seperti yang terlihat pada gambar di samping, kemudian refleksikan setiap petak tersebut berdasarkan titik pusat persegi.<br /><br />Perhatikan bagaimana 1, 4, 5, 8, ..., 64 bisa berpindah...<br /></td></tr></tbody></table>Sekarang, coba lakukan dengan persegi 12x12. Hasilnya sbb:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiZJkhUjUAN52G-VPapgjVeTKjOiTr9WQxDB-zt-PWlu2N0mXDxC0roHLjCv348FL6vZaG1secZynKgYAWxDmyeL2bfXyQObbog7JTZEOT7kxOpy4yq8PeKVulF-nAiG3EQhpz0wzDBu05/s1600-h/12x12.JPG"><img style="cursor: pointer; width: 364px; height: 270px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiZJkhUjUAN52G-VPapgjVeTKjOiTr9WQxDB-zt-PWlu2N0mXDxC0roHLjCv348FL6vZaG1secZynKgYAWxDmyeL2bfXyQObbog7JTZEOT7kxOpy4yq8PeKVulF-nAiG3EQhpz0wzDBu05/s400/12x12.JPG" alt="" id="BLOGGER_PHOTO_ID_5422138677144221154" border="0" /></a><br /></div><br /><div style="text-align: justify;">Salah satu kelemahan metode Lozenge ini adalah kita sulit menentukan pola refleksinya, terutama untuk persegi-persegi besar. Tidak ada aturan khusus yang menentukan polanya. Lebih jauh lagi, kita dapat menentukan polanya lebih dari 1 macam. Ada banyak sekali pola yang dapat dibentuk. Silakan bereksperimen sendiri. :D<br /></div><br /><hr /><div style="text-align: center;"><span style="font-weight: bold; color: rgb(255, 255, 255);"><span style="background: rgb(48, 126, 244) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span style="font-size:130%;">Conway LUX Method</span></span></span><br /></div><br />Metode ini hanya berlaku bagi persegi (4m+2) misalnya 6, 10, 14, dan seterusnya.<br />Metode ini menggunakan prinsip Siamese Method yang dimodifikasi..<br /><br />Mengapa dinamakan LUX. Perhatikan sekumpulan array berikut.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIea8XF8V7LVUVK1rZX750-3MJqHS3I9Zgl8sSYu8uHH9azObDk7Bl1TJ1zQvW3-cjUH-Hj2DqUTP8zD65QMZvvyuewFZ7sjND97kJSL3k0WdW4Ujc4ZddBNzuZNKwbzNXhv293PSWGCl-/s1600-h/LUX.JPG"><img style="cursor: pointer; width: 400px; height: 80px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIea8XF8V7LVUVK1rZX750-3MJqHS3I9Zgl8sSYu8uHH9azObDk7Bl1TJ1zQvW3-cjUH-Hj2DqUTP8zD65QMZvvyuewFZ7sjND97kJSL3k0WdW4Ujc4ZddBNzuZNKwbzNXhv293PSWGCl-/s400/LUX.JPG" alt="" id="BLOGGER_PHOTO_ID_5422145886664848546" border="0" /></a><br /></div><div style="text-align: justify;">Perhatikan urutannya. Ternyata urutan menulisnya mirip seperti kita menulis huruf L, U, dan X. Jika sudah paham konsep LUX ini, langsung saja kita ke langkah-langkah algoritma LUX method. :)<br /></div><br />Langkah-langkahnya:<br /><table align="center" border="0"><tbody><tr><td valign="top">1. </td><td>Bagilah persegi menjadi sekumpulan petak 2x2.</td></tr><tr><td valign="top">2. </td><td>Dari petak-petak itu, berikan tanda sbb:<br />(m+1) baris pertama adalah L.<br />1 baris berikutnya adalah U.<br />(m-1) baris terakhir adalah X.<br /><br />Kemudian, tukarlah petak U di tengah dengan L di atasnya.<br /></td></tr><tr><td valign="top">3. </td><td>Kerjakan dengan Siamese Method yang general. Angka 1 dimulai dari petak teratas.<br /></td></tr></tbody></table><br />Kalau dilihat dari bahasanya, mungkin pada bingung. Oleh karenanya, langsung saja kita ke contoh.<br /><br /><span style="font-weight: bold;">Persegi 10x10.</span> (Artinya m=2, karena 4m + 2 = 10)<br /><table align="center" border="1" width="90%"><tbody><tr><td valign="top">1. </td><td>Bagilah 10x10 menjadi sekumpulan petak 2x2.<br /><br />m+1 baris pertama adalah L.<br />1 baris berikutnya adalah U<br />m-1 baris berikutnya adalah X.<br /><br />Tukar U yang di tengah dengan petak di atasnya.<br />Proses ini menghasilkan sbb:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipwn4SRQjsV68yXIAKMGNUT_ivlA-6OXYbPmrHrvalAZeNRH4pWYmGnJRJXeZfiIUM7HL5qoO2M-lOWM-n9tlcoUj__j_4GvioN77Jl1O4Enn3-r-8XJIlm8IsEn_INXz8FizFcoiFbHsJ/s1600-h/10x10.JPG"><img style="cursor: pointer; width: 307px; height: 228px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipwn4SRQjsV68yXIAKMGNUT_ivlA-6OXYbPmrHrvalAZeNRH4pWYmGnJRJXeZfiIUM7HL5qoO2M-lOWM-n9tlcoUj__j_4GvioN77Jl1O4Enn3-r-8XJIlm8IsEn_INXz8FizFcoiFbHsJ/s400/10x10.JPG" alt="" id="BLOGGER_PHOTO_ID_5422176663788149170" border="0" /></a><br /></div><br /></td></tr><tr><td valign="top">2. </td><td>Selanjutnya, gunakan metode Siamese untuk 5x5.<br />Perhatikan aturan LUX di tiap petak.<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2oVLImBj7zXberr-n9Bouv6CiB7VI3rB4Ym23LtPWU080U5AHjnFxWixLeeKByg2FI9Y7_wwfGUY4J7NEBhWylbEyVp8M7EcPxT19UWI7ixhp5dA72YM6XTp-t8gq6wOIcBx3znl9DRxu/s1600-h/10x10+middle.jpg"><img style="cursor: pointer; width: 308px; height: 229px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2oVLImBj7zXberr-n9Bouv6CiB7VI3rB4Ym23LtPWU080U5AHjnFxWixLeeKByg2FI9Y7_wwfGUY4J7NEBhWylbEyVp8M7EcPxT19UWI7ixhp5dA72YM6XTp-t8gq6wOIcBx3znl9DRxu/s400/10x10+middle.jpg" alt="" id="BLOGGER_PHOTO_ID_5422180512218774610" border="0" /></a><br /></div><br />Hasil akhir persegi ajaib dengan metode LUX:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJCrXZLD2seZZoxT3EIjorOg5r62JVt2VIn_m7q8usRuIkYVn6cv3CUqWsmSmI4cSd3F2guEMGS_ILGMu8lHPuKnZI4FecgNToxw3OC088bLCAZf48a1vuqjqg85lQ1Cyi93wDVyEFx0og/s1600-h/10x10+end.JPG"><img style="cursor: pointer; width: 307px; height: 228px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJCrXZLD2seZZoxT3EIjorOg5r62JVt2VIn_m7q8usRuIkYVn6cv3CUqWsmSmI4cSd3F2guEMGS_ILGMu8lHPuKnZI4FecgNToxw3OC088bLCAZf48a1vuqjqg85lQ1Cyi93wDVyEFx0og/s400/10x10+end.JPG" alt="" id="BLOGGER_PHOTO_ID_5422180515205972146" border="0" /></a><br /></div></td></tr></tbody></table><br /><hr /><div style="text-align: center;"><span style="font-weight: bold; color: rgb(255, 255, 255);"><span style="background: rgb(48, 126, 244) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><span style="font-size:130%;">Strachey Method</span></span></span><br /></div><br /><div style="text-align: justify;">Ini adalah metode terakhir yang akan kita bahas. Cukup ribet, namun sesungguhnya mudah. Metode ini hanya berlaku bagi persegi 4m + 2 (seperti halnya LUX), misalnya 6x6, 10x10. Metode ini juga menggunakan metode Siamese yang dimodifikasi.<br /></div><br />Kita langsung saja gunakan contoh, untuk persegi 10x10. (m=2 karena 4m +2 = 10)<br /><table align="center" border="1" width="90%"><tbody><tr><td valign="top">1. </td><td>Bagi persegi menjadi 4 bagian ABCD dengan urutan:<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcoM3LMW-ov1STF8ViNW5VPjAbQ_DQs2H5512wnSI6X3DIPZuwdVT685_5bTALE1N8vbhIvz4i37OtDLVET39xfWANdI5_AtyEnS41QrAD_JbMIMfNI7feX01X-pdeh7LXaMTv6betV4A9/s1600-h/abcd.JPG"><img src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcoM3LMW-ov1STF8ViNW5VPjAbQ_DQs2H5512wnSI6X3DIPZuwdVT685_5bTALE1N8vbhIvz4i37OtDLVET39xfWANdI5_AtyEnS41QrAD_JbMIMfNI7feX01X-pdeh7LXaMTv6betV4A9/s400/abcd.JPG" alt="" id="BLOGGER_PHOTO_ID_5422184096070798178" style="cursor: pointer; vertical-align: -15pt; width: 64px; height: 50px;" border="0" /></a><br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXpsFNcKwZ1xQ2fKVn-VdNWBeuEWEwpvSmKgIetBWr6myjUxZ7OdyDo998TuKOXyJpHN4cSelvTxk-COKj0A9n512r2MjXTN-TJQZFCfmoWwHRsOd01hFZFw1obK2TnyEaJRoIxk4tjO5K/s1600-h/abcd2.JPG"><img style="cursor: pointer; width: 308px; height: 228px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXpsFNcKwZ1xQ2fKVn-VdNWBeuEWEwpvSmKgIetBWr6myjUxZ7OdyDo998TuKOXyJpHN4cSelvTxk-COKj0A9n512r2MjXTN-TJQZFCfmoWwHRsOd01hFZFw1obK2TnyEaJRoIxk4tjO5K/s400/abcd2.JPG" alt="" id="BLOGGER_PHOTO_ID_5422184949646128146" border="0" /></a><br /></div></td></tr><tr><td valign="top">2. </td><td>Dengan metode Siamese, isilah:<br />1 s/d 25 di A<br />26 s/d 50 di B<br />51 s/d 75 di C .<br />76 s/d 100 di D<br /><br />Hasil:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKI-fbpQB91MmxX0hhglGuTpbYzzI3NsQgz_Kv0B99OKFHH7qJFGO9tz1fhBt5xhoUl_KgR8XMHWVAgKHYKqgX7lAe9vRex-09cRoc-5yLDwaepctm2r_i9j4Hn0F_tD7-FtVWspgBGf3y/s1600-h/strachey+1.JPG"><img style="cursor: pointer; width: 308px; height: 226px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKI-fbpQB91MmxX0hhglGuTpbYzzI3NsQgz_Kv0B99OKFHH7qJFGO9tz1fhBt5xhoUl_KgR8XMHWVAgKHYKqgX7lAe9vRex-09cRoc-5yLDwaepctm2r_i9j4Hn0F_tD7-FtVWspgBGf3y/s400/strachey+1.JPG" alt="" id="BLOGGER_PHOTO_ID_5422187756509992690" border="0" /></a><br /></div></td></tr><tr><td valign="top">3. </td><td>Tukar m kolom pertama dari A dengan m kolom pertama dari D.<br />Tukar (m-1) kolom terakhir dari B dengan (m-1) kolom terakhir dari C.<br /><span style="font-size:85%;">Note: m=2 karena 4m +2 = 10</span><br /><br />Hasilnya:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQBNJHPH14aqaGnLHsiKsNFHYLS045YvPD9w3U1tE1sjgZKYczVMH9HwZDd81aGhVPT3_G_ByKRO_O1kNtqGydey6fU1zkNNEAReQuwD7oUE0XECq_ukgand8zK9Cv-N5-WvbAtFpAOsUZ/s1600-h/strachey3.jpg"><img style="cursor: pointer; width: 400px; height: 222px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQBNJHPH14aqaGnLHsiKsNFHYLS045YvPD9w3U1tE1sjgZKYczVMH9HwZDd81aGhVPT3_G_ByKRO_O1kNtqGydey6fU1zkNNEAReQuwD7oUE0XECq_ukgand8zK9Cv-N5-WvbAtFpAOsUZ/s400/strachey3.jpg" alt="" id="BLOGGER_PHOTO_ID_5422190608597545874" border="0" /></a><br /></div></td></tr><tr><td valign="top">4. </td><td>Tukar petak barisan tengah paling kiri di A dengan sel yang sesuai di D.<br />Tukar petak yang tepat di tengah-tengah A dengan sel yang sesuai di D.<br /><br />Akan menghasilkan hasil akhir sebagai berikut.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUoL7HwLeJnJIxMkC7wce3lvMa9tIP8Ji486kkc43bJ5lH5_BSLOv_DkgNZV-RVNdHE2zjHHODdipB7AFF-uWYJ_onY3WmaVyLVn1fsEbbCDbZ-n-v-7k0BXnDgpu4gGsuLNcKof-5dzxT/s1600-h/strachey4.jpg"><img style="cursor: pointer; width: 348px; height: 224px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUoL7HwLeJnJIxMkC7wce3lvMa9tIP8Ji486kkc43bJ5lH5_BSLOv_DkgNZV-RVNdHE2zjHHODdipB7AFF-uWYJ_onY3WmaVyLVn1fsEbbCDbZ-n-v-7k0BXnDgpu4gGsuLNcKof-5dzxT/s400/strachey4.jpg" alt="" id="BLOGGER_PHOTO_ID_5422192728453028194" border="0" /></a><br /></div></td></tr></tbody></table><br />=======================================================================<br /><div style="text-align: center;"><span style="font-size:130%;"><span style="font-weight: bold;">CLOSING</span><br /></span></div><br /><div style="text-align: justify;">Dalam mengkonstruksi magic square, kita menggunakan metode yang tergantung dari besaran perseginya:<br />1. Untuk persegi ganjil (3x3, 5x5, 7x7, ...), gunakan Siamese Method<br />2. Untuk persegi 4m (4x4, 8x8, 12x12, ...), gunakan Lozenge Method<br />3. Untuk persegi 4m+2 (6x6, 10x10, 14x14, ...), gunakan LUX atau Strachey Method<br /><br />Sebenarnya, masih banyak metode lain yang digunakan untuk mengkontruksi magic square, misalnya Medjig Method, Bree/Ollerenshaw Method, dan sebagainya. Bahkan ada cara matematika tersendiri dalam mengkonstruksi magic square. Bisa kalian lihat di sumber-sumber di bawah. Lihat juga buku tentang Magic Square yang sungguh lengkap dan *bikin pusing* karya W.S. Andrews tahun 1917. Bisa kalian download di bawah ini:<br /><br /><div style="text-align: center;"><span style="text-decoration: underline;"></span><a href="http://pdfdatabase.com/index.php?q=Magic_Squares_Cubes_Andrews_edited.pdf&filetype=0">Magic Square Book by W.S. Andrews </a><br />(24 MB)<br /></div><br />Sekian dolo yach. Si pemilik blog mau kabur. :P.<br />Ada yang ingin ditanyakan, silakan tanya di comment di bawah aja. :)<br /><br /></div><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber:<br /><a href="http://en.wikipedia.org/wiki/Magic_square">http://en.wikipedia.org/wiki/Magic_square</a><br /><a href="http://en.wikipedia.org/wiki/Strachey_method_for_magic_squares">http://en.wikipedia.org/wiki/Strachey_method_for_magic_squares</a><br /><a href="http://en.wikipedia.org/wiki/Siamese_method">http://en.wikipedia.org/wiki/Siamese_method</a><br /><a href="http://en.wikipedia.org/wiki/Conway%27s_LUX_method_for_magic_squares">http://en.wikipedia.org/wiki/Conway%27s_LUX_method_for_magic_squares</a><br /><a href="http://www.his.kanazawa-it.ac.jp/%7Epoyo/magic/concentric/concentricMSs.html">http://www.his.kanazawa-it.ac.jp/~poyo/magic/concentric/concentricMSs.html</a><br /><a href="http://www.xs4all.nl/%7Ethospel/siamese.html">http://www.xs4all.nl/~thospel/siamese.html</a><br /><a href="http://mathworld.wolfram.com/MagicSquare.html">http://mathworld.wolfram.com/MagicSquare.html</a><br /><a href="http://www.grogono.com/magic/individual.php">http://www.grogono.com/magic/individual.php</a><br /><a href="http://pdfdatabase.com/index.php?q=Magic_Squares_Cubes_Andrews_edited.pdf&filetype=0">Magic Square Book by W.S. Andrews </a><br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com38tag:blogger.com,1999:blog-8125318493233557109.post-8274611715485708912009-12-27T12:46:00.045+07:002009-12-27T19:23:39.511+07:00Inclusion Exclusion Principle: Matching Problem<div style="border: 6px groove rgb(240, 108, 20); padding: 5px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Jangan ngeri dulu ngeliat judulnya yang ribet. Sebetulnya ini prinsip inklusi eksklusi ini mudah. Langsung aja kita lihat contoh kasus "<span style="background: rgb(101, 255, 80) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Matching Problem</span>".<br /><div style="text-align: justify;"><blockquote>Ada 10 bola dan 10 kotak. Setiap bola diberi label 1, 2, 3, ..., 10. Begitu pula dengan kotaknya, diberi label 1, 2, 3, ..., 10. Budi menaruh masing-masing bola ke masing-masing kotak secara acak, sehingga sekarang setiap kotak berisi masing-masing satu bola.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNNBvhC7rIbqzzsx_kR6pRk_WeyQuLYYfAzTRvr4xrdkZ3_4iLcPQ-uOnr4OeuEbjB4wHGXQ4VRRyofwKstERgfYqpK2OxHLYTU6krYTHDU_TxCXhzhT4CEx6OJDukCp_Q5uFJ1e8f5_1u/s1600-h/matching+problem.jpg"><img style="cursor: pointer; width: 287px; height: 257px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNNBvhC7rIbqzzsx_kR6pRk_WeyQuLYYfAzTRvr4xrdkZ3_4iLcPQ-uOnr4OeuEbjB4wHGXQ4VRRyofwKstERgfYqpK2OxHLYTU6krYTHDU_TxCXhzhT4CEx6OJDukCp_Q5uFJ1e8f5_1u/s400/matching+problem.jpg" alt="" id="BLOGGER_PHOTO_ID_5419835780644936914" border="0" /></a><br /></div>Pertanyaannya: Berapakah peluang tidak ada satu pun label bola dan kotaknya yang cocok? (misalnya seperti ilustrasi di atas).<br /></blockquote></div>Soal di atas identik dengan soal berikut:<br /><blockquote><div style="text-align: justify;">Seorang guru ingin mengembalikan sejumlah N PR (pekerjaan rumah) ke N siswa secara acak. Berapakah peluang bahwa tak ada satupun siswa yang mendapatkan PR-nya sendiri? Jika N adalah 30? Apa yang terjadi jika N lebih besar atau lebih kecil?<br /></div></blockquote></div><span class="fullpost">=======================================================================<br /><div style="text-align: center; font-weight: bold;"><span style="font-size:130%;">PENYELESAIAN</span><br /></div>Jawabannya adalah <img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDzoDrw5K6gsmbiItQ3LOcS9JtpWOSDQLw9ch6lkuBPDJQL2fdrEEzDeRgQvTQL7bMdJd3GDhymvS4Yz8Mj0nRBqO0qT-xPACWUgxCPlUc51Lcb0-Yg68AE6umVgU0aWb2kNh4wnCXmkpE/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5419843571702362866" border="0" />.<br /><div style="text-align: justify;">Yang mengejutkan adalah peluangnya cenderung mendekati <img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgfoJQB8B8oJKzKke6-aNBauc8hNi1yCnjgiNbi4BIh_Dw6WKQFbDjj7QKBEC1xAzAiKMtHwKEoFw6r8w4XDunSwQnKfobI-eWsTE7JJxH8xeJHEkLlr586ggY8p1w-Lu-YrQtOgJLEAku/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419843115312057554" border="0" /> atau sekitar <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmlwA8G-qq-vpRmbIcYErYieCII86tKNjjDhnO9i_847Qge2ggegzkQ3yAfNYosOVK59o83vlWElBUPt-XgOxHeyTFFQ5RF5SiU5KpBs0o-JnMmZFiwfAY8w9w5wWnhFTBgGcPzEKpqEuM/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419843112767682338" border="0" />, berapapun nilai N yang ingin kita ambil, asalkan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj70BbWpsI04N95HooJsHYHpnpumT7qqV1i1gb14EaT49Mu2gQYErpXcueJDxKrIr_8WPKMQkVxb9f6Vk8mOLxC-TClS43Mw2xqFutvcGFYm-73Y9DjqGR6hY179ZJNECEAIj3r5W2klTHA/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5419843794400625570" border="0" />. Silakan dicek sendiri dengan memasukkan nilai N ke fungsi di atas.. Lebih jauh, silakan kalian bereksperimen sendiri dengan memisalkan N, misalnya 3, 4, 5, dan seterusnya.. Lalu, bagaimana hasil tersebut didapat? Bagaimana tiba-tiba muncul nilai <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhctkwTlRr4uacM6qM2dnYO1H54VPxsb1a96ZXCGTueOo9YsZGgF9nPfhzNoH5ECWf26AIVoRV_dxRR45AjXbwm0MkCqRJfIpyYxHUviFlljKWAyDa_vvwcpQtiSCgvW8tN6mWKIj258Ymi/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5419885890122966258" border="0" /> ini? Lihat lanjutannya di bawah. :)<br /></div><br /><hr /><div style="text-align: center; color: rgb(204, 0, 0);"><span style="font-size:130%;"><span style="font-weight: bold;">Prinsip Inklusi-Ekslusi</span></span><br /></div>Cara untuk menyelesaikan kasus ini adalah dengan prinsip inklusi-eksklusi (atau dikenal dengan sieve prinsiple).<br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 10px; margin-left: 50px; margin-right: 50px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"> Inclusion-Exclusion Prinsiple<br /><img style="vertical-align: -17pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp8sq_SCqZ9E7m2SMSTyvDDzIv6_LKnfouHQyHsTb4tR6-qTzFT1Hu14vZ8Ip8oA9o383p-yOjymNj0qeEt9cvD7HCUSnusfR4LAdVIcfJ4YIEO4xaEDcY2Waqb_VvBOWp-akzRn9ly9cI/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419849184274788962" border="0" /><br /><span style="color: rgb(255, 255, 255);">________</span><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaotJSPYE-gBmmr6qmzjUDNy3BvmelSFoGqz6fTlBCjb0CgyOZ4quGPZctAB_v3HnnUMWCYt_wKwodil8MOtQq145IYg2m9rcsh8bbKt4evX-NLF68SdYCdJ_FnghzTZHj0w__Fe7rUoeP/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419849183903419666" border="0" /><br /><br /><span style="color: rgb(255, 255, 255);">________</span><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRa0OMVdeHDRX00khNQbdVNXtwtjGxTpGH491VoKPfc0RoAX-BM5DvQae7ez5ywPCJy_YfopCUs2iBOXzqVc-xySb3vBxcB5M5ZNtv8jXnnFFrTy0JG1uuwTgcqY__07ZSbihhbeLmA0ui/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419849174187920770" border="0" /><br /><br /><span style="color: rgb(255, 255, 255);">________</span><img style="vertical-align: -1pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMSsQGEGfMDDcRmtniKnrn7vg5lQ48m_yepsbzjhsYmsWH2VftWvGuCQa0NJRyW2KO_g6GQgZoiEas-F17DlCic6KWMkFhtmZgeIzeFk20UvIU6uY43KfcxF7sYrQwAiGv54BEsUmmBnIF/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5419849164178985986" border="0" /><br /><span style="color: rgb(255, 255, 255);">________</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTcMM7WETr4lvOoH9APEoF2upn44tpq8Hv2ulrgCj0rDqvv0kr9ki_UEr2ZYtAmKy9oS71bpn-zwOsGZnCqrW6eUjiTUOkXOmYtUkkkv9ZUMsW8kgPw-RT4xPj4YofoP4d5XNiXAQF9HbO/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5419849159800599554" border="0" /></div><div style="text-align: justify;">Kalau kalian melihat di rumus di atas (wikipedia), rumus itu terlihat sangat menakutkan, tapi sesungguhnya mudah sekali dijelaskan dengan *bahasa manusia*.. Nah, di post ini, saya ingin menjelaskannya dengan bahasa yang mudah dimengerti.<br /></div><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 5px; margin-right: 5px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Ambil contoh:<br />Misalkan kita punya 2 himpunan, yaitu himpunan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzNfofR_8sYXBk3vCwHnSDszGBOm5IeX2PVKupeSCcJ76EIuTteJdvszK33SdbEFyyGLQ_RrkYKG9jdSNAfYijmQDkFvPMBjulS8IALo5nvxSPIqtQwKVY4sGR7dJcOqk-QPG2IyQvArCG/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419850852507344242" border="0" /> dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip1x-5kAxwEJsNcnVgmewexiZAet-j7rzJSfjEQyOxSip3Z7Mc-GO4AvNwz6BT6X-EJvtVbeq8qrDqajPrzqTlmeoMYPFUT-z3fTsUy4HQ4OmIJTas3ehPTNG3QP4p1YasVWlLOYKkbgld/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419850849581423330" border="0" />.<br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Nzup4DpRRZnvjva1ioBm01XjBq62gkYjx7Fke97MsJTszHfsLhxJUMqqtWsshYowHhTuAxvWWEUCfy4pCFaKSiTX-UBM3QFreJ4-_B8c3wGDqwSHSc1URIwrliBDQ3Y1DhBPLFloX-Bj/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419851732067745890" border="0" />.<br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFt43cowmeg0htATT1_vFzmLKGSaZFJGoG4u1Qjup0mYME6bb20Nigjb21wwSlKJtLJQao2_1B4kLF-CWhuyeyW70LJKRvlFPaKcJsNC-3XnPCJDKGzy7e1cLbR4LcDm5WAux5CQyTjv0p/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5419852064148903218" border="0" />.<br />Untuk menentukan jumlah anggota <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRusHcRAh_wN-5rC9RIZ4gfGc2ISgPwymXjJyr4e7YTTba6DOHFQ7v2SbqC5zE-n7q6hyxNDF73LDpmqWL8Fue4IKkSiEdfBYYQYJa-G16BkVsg4utIdKM9kJupyiYkr27o0QlCiB68dqw/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5419852389435217298" border="0" />, kita gunakan formula berikut:<br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiocyH5e-Etvi5HFFukUzkSkW7D8w2WSjov-2oXhhdzSvQFuWiQAWIg7GRuuR7NmEE_GlFCWN46pI0MEUOmWZF4_nMwbZE4UwgYptZ2s80U2zsV2Hww4btmJ5acmWuzr9va_X_6T_dsJUUN/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5419853842101985986" border="0" /><br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhR46aEI3sSbulebFdKs_E90Fq_YVlvOvytG8FmUZQagyb_48dh2pgNtNVtkMa2iLjo8Gs0SUNbc9pL-vl9_Qwrtd9ozadig8eiv8HNqposVNtlpXh4zO80T3ZQcqyJ48SnhsmZwKoiyjLt/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5419853536316681554" border="0" /><br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDQeZhD0UQnrywTTnCrbO3tEgAU-duQctEl7O31s6Bwa4THzPwsa5pbLAKIYXJ_VfYT1PtE6HGyx9HpF9cld6TI58P4BRXqFjgImhr2cT7d1c1wxiUmxbAYiOinMignWzG_pzqWdn5hgUk/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5419853526374072242" border="0" /><br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgj-PdpTzMNa2ytb2vMWSSTNROl3Mdn8f_MKvUeJZUZo_91JB39JAx43be2iBnXX9SL5EYwwmd2TtX_KzqHPRaXZcImRIg0FOjpFt3vpESkmnfa73tFkjH3Z6_PQ064ebX7zOJ2MXTu_lRm/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5419853521011876322" border="0" /><br />Jika digambarkan di diagram Venn adalah sbb:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNhP1uFYCVFgQ3GMPvXJJaXO0bSm3ATs50TmUGObpI29bYmY8qkSDpsSVq-ZWmh60V3WiXX89u_ar9l9M5VMqPKX7-njhoWmx7JVCvwzboNerNSmJSwwwr5AxgSlxBgAUH094diJgrGDeS/s1600-h/Diagram+Venn+Ai+A2.jpg"><img style="cursor: pointer; width: 179px; height: 91px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNhP1uFYCVFgQ3GMPvXJJaXO0bSm3ATs50TmUGObpI29bYmY8qkSDpsSVq-ZWmh60V3WiXX89u_ar9l9M5VMqPKX7-njhoWmx7JVCvwzboNerNSmJSwwwr5AxgSlxBgAUH094diJgrGDeS/s400/Diagram+Venn+Ai+A2.jpg" alt="" id="BLOGGER_PHOTO_ID_5419856086962123298" border="0" /></a><br /></div></div><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 5px; margin-right: 5px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Ambil contoh lagi:<br />Misalkan kita punya tiga himpunan, yaitu <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzNfofR_8sYXBk3vCwHnSDszGBOm5IeX2PVKupeSCcJ76EIuTteJdvszK33SdbEFyyGLQ_RrkYKG9jdSNAfYijmQDkFvPMBjulS8IALo5nvxSPIqtQwKVY4sGR7dJcOqk-QPG2IyQvArCG/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419850852507344242" border="0" />, <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip1x-5kAxwEJsNcnVgmewexiZAet-j7rzJSfjEQyOxSip3Z7Mc-GO4AvNwz6BT6X-EJvtVbeq8qrDqajPrzqTlmeoMYPFUT-z3fTsUy4HQ4OmIJTas3ehPTNG3QP4p1YasVWlLOYKkbgld/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419850849581423330" border="0" />, dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXNMZbJYvruvU13qbKpqFYW0WNT9CD7RtYWeFgH2qRmgFg4RDESA6cQlpoxFI3ohN7h96FNbgQP7DUwugFw5FcLc-MvpazGOEJDeToejQ_jnCGivD6Xr2tyOnqXuXXmkQ-MLZqnjQ18tbn/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5419856404381100322" border="0" />.<br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Nzup4DpRRZnvjva1ioBm01XjBq62gkYjx7Fke97MsJTszHfsLhxJUMqqtWsshYowHhTuAxvWWEUCfy4pCFaKSiTX-UBM3QFreJ4-_B8c3wGDqwSHSc1URIwrliBDQ3Y1DhBPLFloX-Bj/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419851732067745890" border="0" />.<br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFt43cowmeg0htATT1_vFzmLKGSaZFJGoG4u1Qjup0mYME6bb20Nigjb21wwSlKJtLJQao2_1B4kLF-CWhuyeyW70LJKRvlFPaKcJsNC-3XnPCJDKGzy7e1cLbR4LcDm5WAux5CQyTjv0p/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5419852064148903218" border="0" />.<br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4KSna-iAp8RHZ1efk-4mWj_Rxerp3WzWDu0O7aOGL701z6Mh-1yNbFA4r1nxC6gj0BMdl5LQGfLUkndzcfh1ErJuvY-XOOSYhN8JUDYuXyKeI5Agg-S2TlYTRaX5usWuiYb3zCOByr38u/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5419856765994110946" border="0" /><br />Untuk menentukan jumlah anggota <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEignOE8HfqWBlNQTsMfTwqW1tp75-cS9w2jik1Klt8mleCs2HtlxIexRDNCn_kABGK8vXiV60iQA5E5aKJA3eN_ARFV3sEmkIGnpZipdGuOljEiFvy89_GprqGmhfxQt70y4n2v24-DZ3lE/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5419857059173364258" border="0" />, kita gunakan formula berikut:<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg24zsiVcWPPnT0q_ujQI_CXKP2Q_CfhhdXfrcqQlA7Zh0yS1brQjNsFimJB1dtysCJq4Cl62kd0LqEYP9qCiZi_BOPXuwaZ44iZBRoz-EtFpOftsOdvqQV91FEWoJx-PMucEnKZBUZE6ou/s800/13.gif" alt="" id="BLOGGER_PHOTO_ID_5419857956846497570" border="0" /><br /><img style="vertical-align: -4pt; width: 650px; height: 17px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5M2Z8FPi4SNWDHeuoi1TNXcG0sufJJUvbkW8dN8KknFz8o9hoHHrabOW3NpN4kFkM0qA0WG4AXSl2cdH33k4GiDgL2gRtMASgqxOfjVj326blKDc4umvztdnFGlgLMTiZ7gTDcTjA6qpF/s800/14.gif" alt="" id="BLOGGER_PHOTO_ID_5419858669849698674" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPBI7UjTVjK94pvvqVA3heNPPNq3EtnkEmwkCh22rvza4RmVXjnfuhKe_zwEo7v9-Ta3V53h53CMsNIerINNwV9SshZJadqE8tle8DvbnJXEXmBge9aeIeCIxfFsaOS2qwy4x159UyOO-t/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5419859130885577042" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCUcxjzViH2h6M0rwkeBqb5jVUcKkaDoMMG_mSKWjMWeFEK15n17WD91s48h4ST3fYmHitkR0k8vjlt46Kr1iSyZR9OTRVujbHfUOLFoLHzcK4u4dlUv1KhhOAelhSASOMJQfxJpYM2m6v/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5419859118557163218" border="0" /><br />Jika digambarkan di diagram Venn adalah sbb:<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh29q03QIRSvHTMXo_5r1oISP1YurMvkhVRqE42HDPwRfzvdqYqjN0FPT4A8t9HczoY0PkzYpuLP79FGenhrWiDGpP6G6wx_NSf9tW6XkF630fq-hT-WWXgQEozHTikFQwICN_lu_3xsYsE/s1600-h/Diagram+Venn+Ai+A2+A3.jpg"><img style="cursor: pointer; width: 172px; height: 139px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh29q03QIRSvHTMXo_5r1oISP1YurMvkhVRqE42HDPwRfzvdqYqjN0FPT4A8t9HczoY0PkzYpuLP79FGenhrWiDGpP6G6wx_NSf9tW6XkF630fq-hT-WWXgQEozHTikFQwICN_lu_3xsYsE/s400/Diagram+Venn+Ai+A2+A3.jpg" alt="" id="BLOGGER_PHOTO_ID_5419856090583136946" border="0" /></a><br /></div></div><br /><div style="text-align: justify;">Pahami terlebih dahulu bagian yang di atas, karena sesungguhnya prinsipnya sangat mudah.<br /></div>Untuk seterusnya, misalkan n = 4, berarti ada 4 himpunan, maka formulanya adalah sbb:<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPM-c_3PPvc-gLLy0aFAOI-lobPFSw3pN53wq6fz7F2O8ZQvh5HgtV0vj0j19Kw6Ui6d574CZurR0GDxB6PCe1RrABmwXcpwANQiSBOnjVlAahoThCbiyzE1WznWUWTjJYjogOIBjIhkPG/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5419861202268023042" border="0" /><br /><span style="color: rgb(255, 255, 255);">________________</span><img style="vertical-align: -4pt; width: 502px; height: 17px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjg1tUM_fblg8-15u1oyrS8n0JOkgHHZ6iNRHnxZMdn1Q0ngb7VdOuJNVgpXWIEQsLRxXPryxgd5lqWAJ1BxDt_sM7RDnoUDaVUQPPPyLdnyDio9BzH8aMNBGI-uy4sYhpUjVdlgO1aHy7B/s800/18.gif" alt="" id="BLOGGER_PHOTO_ID_5419861196071168242" border="0" /><br /><span style="color: rgb(255, 255, 255);">________________</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8tFH6TduOoF90uYSu06nBO8SfFk_PZfa0ULmr1y6QJQ-GdSSLxBIEo9R03X3ixdwAb9oxyq4aCwnF4k_wzaAD7i56EvNYZKbiGw79LKbn29PFKxRNTQNz9K8aiXk-gT1EeEwW-u3bMXvO/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5419861190276854418" border="0" /><br /><span style="color: rgb(255, 255, 255);">________________</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirdsxBGeFXRJpH7KIBZZzfw49oG12Tsek0AMxEb3rKROp8ClZ4Ui5rsL084QBUY4Bnia2W7FUVf3XYyQYAXxVpOPmAcbeTh-kkZttZF-MY23WjiI3Y3VvS3LE08POmCkTfGC2LTiNGk2Ot/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5419861175697441154" border="0" /><br /><br /><div style="text-align: justify;">Perhatikan bahwa tandanya berselang-seling, dari + ke -, lalu ke + dan ke - lagi. Ini dapat dibuktikan secara prinsip logika. Untuk selanjutnya, kita gunakan singkatan untuk penulisan formula di atas dengan notasi sigma dan pi sbb:<br /><br /></div><img style="vertical-align: -17pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp8sq_SCqZ9E7m2SMSTyvDDzIv6_LKnfouHQyHsTb4tR6-qTzFT1Hu14vZ8Ip8oA9o383p-yOjymNj0qeEt9cvD7HCUSnusfR4LAdVIcfJ4YIEO4xaEDcY2Waqb_VvBOWp-akzRn9ly9cI/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419849184274788962" border="0" /><img style="vertical-align: -18pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaotJSPYE-gBmmr6qmzjUDNy3BvmelSFoGqz6fTlBCjb0CgyOZ4quGPZctAB_v3HnnUMWCYt_wKwodil8MOtQq145IYg2m9rcsh8bbKt4evX-NLF68SdYCdJ_FnghzTZHj0w__Fe7rUoeP/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419849183903419666" border="0" /> <img style="vertical-align: -18pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRa0OMVdeHDRX00khNQbdVNXtwtjGxTpGH491VoKPfc0RoAX-BM5DvQae7ez5ywPCJy_YfopCUs2iBOXzqVc-xySb3vBxcB5M5ZNtv8jXnnFFrTy0JG1uuwTgcqY__07ZSbihhbeLmA0ui/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419849174187920770" border="0" /><br /><br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -1pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMSsQGEGfMDDcRmtniKnrn7vg5lQ48m_yepsbzjhsYmsWH2VftWvGuCQa0NJRyW2KO_g6GQgZoiEas-F17DlCic6KWMkFhtmZgeIzeFk20UvIU6uY43KfcxF7sYrQwAiGv54BEsUmmBnIF/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5419849164178985986" border="0" /> <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTcMM7WETr4lvOoH9APEoF2upn44tpq8Hv2ulrgCj0rDqvv0kr9ki_UEr2ZYtAmKy9oS71bpn-zwOsGZnCqrW6eUjiTUOkXOmYtUkkkv9ZUMsW8kgPw-RT4xPj4YofoP4d5XNiXAQF9HbO/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5419849159800599554" border="0" /><br /><br /><hr /><div style="text-align: center;"><span style="color: rgb(204, 0, 0);font-size:130%;" ><span style="font-weight: bold;">Penyelesaian dengan Prinsip Inklusi-Eksklusi</span></span><br /></div><br />Kita gunakan kasus bola dan kotak. Misalkan ada N bola dan N kotak.<br />Kita definisikan set-set himpunan sebagai berikut:<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzNfofR_8sYXBk3vCwHnSDszGBOm5IeX2PVKupeSCcJ76EIuTteJdvszK33SdbEFyyGLQ_RrkYKG9jdSNAfYijmQDkFvPMBjulS8IALo5nvxSPIqtQwKVY4sGR7dJcOqk-QPG2IyQvArCG/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419850852507344242" border="0" /> = himp semua urutan dimana urutan pertama pasti benar (bola 1 berpasangan dg kotak 1).<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip1x-5kAxwEJsNcnVgmewexiZAet-j7rzJSfjEQyOxSip3Z7Mc-GO4AvNwz6BT6X-EJvtVbeq8qrDqajPrzqTlmeoMYPFUT-z3fTsUy4HQ4OmIJTas3ehPTNG3QP4p1YasVWlLOYKkbgld/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419850849581423330" border="0" /> = himp semua urutan dimana urutan kedua pasti benar (bola 2 berpasangan dg kotak 2).<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXNMZbJYvruvU13qbKpqFYW0WNT9CD7RtYWeFgH2qRmgFg4RDESA6cQlpoxFI3ohN7h96FNbgQP7DUwugFw5FcLc-MvpazGOEJDeToejQ_jnCGivD6Xr2tyOnqXuXXmkQ-MLZqnjQ18tbn/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5419856404381100322" border="0" /> = himp semua urutan dimana urutan ketiga pasti benar (bola 3 berpasangan dg kotak 3).<br />....<br />dan seterusnya.<br /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKmM99tvZsNIM5JqaSLVh4oPShvDTAX0voHIoMuF54jDegKtYTfLr8y_UVRDDe6LCCyjgAAkkca7a2bmTyfGx9sVA0Vu95zBjtLwkEB1Brs0xqnKusaQphFVAXqR2lLn5ZIs-cL7sJvuqm/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5419867599792052066" border="0" />= himpunan semua urutan dimana setidaknya ada 1 urutan (bola dan kotak) yang pasti cocok.<br /><br />Kita gunakan prinsip inklusi-eksklusi untuk menentukan nilai <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKmM99tvZsNIM5JqaSLVh4oPShvDTAX0voHIoMuF54jDegKtYTfLr8y_UVRDDe6LCCyjgAAkkca7a2bmTyfGx9sVA0Vu95zBjtLwkEB1Brs0xqnKusaQphFVAXqR2lLn5ZIs-cL7sJvuqm/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5419867599792052066" border="0" />.<br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKmM99tvZsNIM5JqaSLVh4oPShvDTAX0voHIoMuF54jDegKtYTfLr8y_UVRDDe6LCCyjgAAkkca7a2bmTyfGx9sVA0Vu95zBjtLwkEB1Brs0xqnKusaQphFVAXqR2lLn5ZIs-cL7sJvuqm/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5419867599792052066" border="0" /> = <img style="vertical-align: -17pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp8sq_SCqZ9E7m2SMSTyvDDzIv6_LKnfouHQyHsTb4tR6-qTzFT1Hu14vZ8Ip8oA9o383p-yOjymNj0qeEt9cvD7HCUSnusfR4LAdVIcfJ4YIEO4xaEDcY2Waqb_VvBOWp-akzRn9ly9cI/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419849184274788962" border="0" /><br /><span style="color: rgb(255, 255, 255);">___________</span><img style="vertical-align: -18pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaotJSPYE-gBmmr6qmzjUDNy3BvmelSFoGqz6fTlBCjb0CgyOZ4quGPZctAB_v3HnnUMWCYt_wKwodil8MOtQq145IYg2m9rcsh8bbKt4evX-NLF68SdYCdJ_FnghzTZHj0w__Fe7rUoeP/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419849183903419666" border="0" /><br /><span style="color: rgb(255, 255, 255);">___________</span><img style="vertical-align: -18pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiRa0OMVdeHDRX00khNQbdVNXtwtjGxTpGH491VoKPfc0RoAX-BM5DvQae7ez5ywPCJy_YfopCUs2iBOXzqVc-xySb3vBxcB5M5ZNtv8jXnnFFrTy0JG1uuwTgcqY__07ZSbihhbeLmA0ui/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419849174187920770" border="0" /><br /><br /><span style="color: rgb(255, 255, 255);">___________</span><img style="vertical-align: -1pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMSsQGEGfMDDcRmtniKnrn7vg5lQ48m_yepsbzjhsYmsWH2VftWvGuCQa0NJRyW2KO_g6GQgZoiEas-F17DlCic6KWMkFhtmZgeIzeFk20UvIU6uY43KfcxF7sYrQwAiGv54BEsUmmBnIF/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5419849164178985986" border="0" /><br /><span style="color: rgb(255, 255, 255);">___________</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTcMM7WETr4lvOoH9APEoF2upn44tpq8Hv2ulrgCj0rDqvv0kr9ki_UEr2ZYtAmKy9oS71bpn-zwOsGZnCqrW6eUjiTUOkXOmYtUkkkv9ZUMsW8kgPw-RT4xPj4YofoP4d5XNiXAQF9HbO/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5419849159800599554" border="0" /><br /><br />Keterangan:<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZzjQPMO1fG5b6ow5NNZWpwjUdSBIIs8_UmMZNuFsG-dyP7RKYr6g-S0rVFrNvdUF8c_zjQilf7xTPZPVHP6PfoUnp3kNgtTdQhKDirxKZY1zkj854pPUpa30AZV3o64qtrz7jL6_a6P2-/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419872316597769938" border="0" /> berarti himpunan semua urutan dimana urutan ke i , j , ... hingga p benar.<br /><br /><div style="text-align: justify;">Sebagai contoh:<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGITc40fIJUZtCkyJXKZkxwr0EtlVXKK-0XQqaNDsHexww7GDmn90DWMRpARB1n2nWEnSvL0vMxnnZjAgxO2Us-kMtjMTe0OOvYKsFA0DT1rS1EWnjLz46qlpXLo92ec32u6YLBaO73c_w/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419873009709761922" border="0" /> berarti himpunan semua urutan dimana urutan ke 2 dan urutan ke 6 pasti benar (bola 2 berpasangan dg kotak 2; bola 6 berpasangan dg kotak 6).<br /><br />Perhatikan bahwa banyaknya himpunan itu tidak bergantung pada letak urutan, tapi hanya bergantung pada banyak urutan yang cocok (k). Sebagai contoh: banyaknya himpunan dimana urutan ke 3,6, dan 10 cocok sama dengan banyaknya himpunan dimana urutan ke 2, 8, 9 cocok, dan juga sama dengan banyaknya himpunan dimana urutan ke 1, 3, 4 cocok. Oleh karenanya, secara logika, kita tahu bahwa setiap notasi sigma dapat direpresentasikan sebagai <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwZXFgKvMKQYIx1y8SpvG9cFB-0Gltm65M83HqDcnCMAmP2Z1L61e25yDFv62K083ug0KeNvUOoIjKj4ETMXh-J3b9wJge5-z8bknGGI4EqLOeb83ALA92mQnueKkbs9sWii13Azw-_dPd/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5419875563844708978" border="0" /> di mana k adalah jumlah urutan yang pasti benar.<br /></div><br />Jadi, formulanya sekarang adl sbb:<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicVdq0IBZ4FCb3ThI8eKTPG1XGZy2w-0p1FwJehNMZMHG7syZTuZKJY78xhT3Wq9d7yYgn6vALLol7RrIxdG6irJHclptp9faFOTm4aKnv_5gO4rGJV24-mLKKNvv1K0b_q5fnCxbnXDEX/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5419877978476258578" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV6weqG_yIcZtv1cRiCGTsdoEUW2nENt4WW6kDvA_gVwJs87lUdwHsnh8aSiE0jTwEbjl4qymXX7KOBmQU5eD7Y8Lk-p3wzcIS8iXgIEag461HGkMY-ikxFDfidGO37N7kfmCb1TocTdXW/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5419877819427382402" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHzNLgua5xGjYHucN3MiI6LSmtYC2VH2-trzHUEnHBpwi2WxW0_CnYNszS1piI7feOnFem4RWmwFsmo7r3__nOVWio2HWAO_cbG0IWPcvxPKPe0Ed1JR3zffGcD3gzePdzXlU-nxH8aXXK/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5419877815489994978" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -1pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdp8Ar4JYNMROh7ni77xICPmkCNaNPtgm12kI60WRDy6XRlHUMxL46vAqF2zpKlaLCcJODnkN7r7BKdtdXx8cIu-xUh7IWd6Ab29_LMqHZIk8ZNQjkEh2daLVCSanWFarVuyGB2j7EdWxv/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5419877811767773314" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnJPi4W5CeC-3c1Yt8Kutr2xxsDQtCeY68VW4bF_G2uGs7gZdY1G-55B0ZsWQEK1qQrRV_QctwGokRDPcnHRnBJy3nLME87D9jnPRFkfQIOVWpLYT_qiqWM6ERqjzwZr7MlGTnUCAGI9sa/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5419877807116065074" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -1pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdp8Ar4JYNMROh7ni77xICPmkCNaNPtgm12kI60WRDy6XRlHUMxL46vAqF2zpKlaLCcJODnkN7r7BKdtdXx8cIu-xUh7IWd6Ab29_LMqHZIk8ZNQjkEh2daLVCSanWFarVuyGB2j7EdWxv/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5419877811767773314" border="0" /><br /><br /><div style="text-align: justify;">Untuk menghitung <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSTQpWi6IngS129gyAMEuTWyd1eHMnPflsX7HhEpO61ExbqivRvEWT9FZ9QJtonKWLee5c16S3TqgDpBc1iDR82rbjCdAcOu1U4omi6pr3xRaS1imqgyZ6ih7evOSBAD5tgXVgflDswU5W/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419879511187114098" border="0" />, kita tahu bahwa dari <span style="font-weight: bold;">n</span> urutan kartu, urutan pertama pasti benar. Oleh karenanya kita tinggal menghitung permutasi sisa urutannya, yaitu <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNPP4LDz_vnK5uuQmw5jeoukG97G1b53w4ZjrRG5xzWHFH1Zbt3hKaupNl0mhurEBaZV2_44oRdKtJmdf-yMT8muYUA2WoneLioZ_WhK_TtHaIQ5-UpBBt9NNjTOZdXHmdv41fZK0cie2v/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419879504073821682" border="0" />.<br /><br />Untuk menghitung <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEingiiRWCup1GlHrTaN-x0hblgvrzUU8a2da8IqZBj56OtgCQwqlar7btSKBrFjfjOh7d9xAZ32s1ssGW1A0YKrc_JAQKDsX4CN5Yeo5M-KwtFBMm-NkxN04lPcB8fJB7XGIdy5kCWVYkNl/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419879911229253474" border="0" />, kita tahu bahwa dari <span style="font-weight: bold;">n</span> urutan kartu, ada <span style="font-weight: bold;">2</span> urutan yang pasti benar (yaitu di urutan pertama dan kedua). Oleh karenanya, banyaknya himpunan ini adalah permutasi sisa urutannya, yaitu <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhea0PjGubhZeo6C8t0LoscVh5zPNTdWmDEuP4UP48WlvbYPY2eeS30jiBizYTYXkg-QYnyQ5sH2lBTlHCrDGGrDOgnsSNVxKwnIIk32NLnBdPJcLTUp5UDMzY7Z_QMc0qwLmS-_KbjCb2x/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5419879905435630034" border="0" />.<br /></div><br />Untuk selanjutnya, memakai konsep yang sama.<br /><br />Dengan demikian:<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzCyFXC-KpXmgcVGKikIsyXlykiXHRfsSXnj6xxQfBQPXN5ZR9rzdv6DbEgVwFzk40GbY38vrnIQPASWbtkUAQWcBRb6FIyhJWYeTzNR9b03g1dnReVYeFj3qvmgp6xNV1alojpSsLUZnh/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5419881006322158754" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikCE20nZ98yNWj7vu0YO_mBcuFhizNpyjhY2sxyOHDjeDea_CC0SkkwUlbFgxYL-GnpN4_eveve5yZZS4ZpDe9eQfh2638_4r8uEAqnzrAMwJnRtKhBIp_Uwi6FMka77AgFVA9gSLk3XGs/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5419880998367937746" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxGU79j4to0bY70zZObLmjzq6bigmvV_ijD3cHykyv9Gi2rP-zhWNIrFhBsA__afMg_8NKnCiIgFutYZaLbkWWDB8TUBO-8qIKDMnFu1eiKX-sdLsryUVOW_fa2yOGHy2bxg2IZ9-M4fLy/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5419880993638518434" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -1pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdp8Ar4JYNMROh7ni77xICPmkCNaNPtgm12kI60WRDy6XRlHUMxL46vAqF2zpKlaLCcJODnkN7r7BKdtdXx8cIu-xUh7IWd6Ab29_LMqHZIk8ZNQjkEh2daLVCSanWFarVuyGB2j7EdWxv/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5419877811767773314" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjD5nyw0-k5sMX0nsWHlAv8V7FvtjnchGNtsxLTYq3WJ8Msj6UIPLT_X7_ZVnAji3ARU3piZwBL0JQhbaGgT6aDx_r1SBcl6iBrca4X4xlsLjU41W3ujlPKgTvexAv7F-AohwFW7XdicjAg/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5419880989510082066" border="0" /><br /><span style="color: rgb(255, 255, 255);">___</span><img style="vertical-align: -1pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdp8Ar4JYNMROh7ni77xICPmkCNaNPtgm12kI60WRDy6XRlHUMxL46vAqF2zpKlaLCcJODnkN7r7BKdtdXx8cIu-xUh7IWd6Ab29_LMqHZIk8ZNQjkEh2daLVCSanWFarVuyGB2j7EdWxv/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5419877811767773314" border="0" /><br /><br />Kita gunakan notasi sigma untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKmM99tvZsNIM5JqaSLVh4oPShvDTAX0voHIoMuF54jDegKtYTfLr8y_UVRDDe6LCCyjgAAkkca7a2bmTyfGx9sVA0Vu95zBjtLwkEB1Brs0xqnKusaQphFVAXqR2lLn5ZIs-cL7sJvuqm/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5419867599792052066" border="0" />:<br /><img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpSk9_IOzrseSlB_G0fkPvdiaV0ZhBGoTjDXFcELt-3EICgIfUNzJPTt2MRkczB8DCLuVACLkADBbCSgjzKO24oy2WIPNwizaYcAJqrihyxYgZ_DZKNLuTAH0sMJFUbEU3lql69b8e2P2w/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5419881781083139746" border="0" /><br />Kita tahu bahwa <img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyLb2xPKAvHWHzkxU2AkbmV8zG7UqaWsbLg480fmKo1ZPPa4KDTKWc0AOeRUVeNvTxmUd2jWjmlBsyRW2u5XXcrjIcYZUK9QCFPIKFBGaMVlFDUQxkKqCsKUDYstCgzq5vjxr19do3Bh_r/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5419882854358773762" border="0" />. Oleh karenanya, <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKmM99tvZsNIM5JqaSLVh4oPShvDTAX0voHIoMuF54jDegKtYTfLr8y_UVRDDe6LCCyjgAAkkca7a2bmTyfGx9sVA0Vu95zBjtLwkEB1Brs0xqnKusaQphFVAXqR2lLn5ZIs-cL7sJvuqm/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5419867599792052066" border="0" /> dapat disederhanakan menjadi:<br /><img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjvRKt3Zit4P1IT1p_9RQ-BCLKPqfwJYZmdjIGGTXtr89_nWeeuCIWK-4SI7kI3dKQV6A06ou0-k5iE_YlJVdojrqICZVIDEJ4ekEEhyphenhypheni00vkDDV7KIazUPsKctw8sQiim_fz2GByK70ZXA/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5419883180293077682" border="0" /><br /><br />Kita tahu banyaknya himpunan yang setidaknya memuat 1 pasang yang cocok. Oleh karenanya, kita dapat menentukan peluangnya.<br /><br /><img style="vertical-align: -10pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWADMth1VWTBEmeqtJ-CzH6UTx3ZH4zJQqOECwu9gZaOqIRs2ovpChA1P0umBfOQDdgtAVGBNaK1wdIRyRQuppL8r2urKYOVpzu1X6IRheQl-lY2LRt3WxnYtn2V4D3zwW3LuGG_o4fBuK/s800/13.gif" alt="" id="BLOGGER_PHOTO_ID_5419884468770472210" border="0" /><br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgilHorHLs8EKUBLpW-VxwpCIjZDOYK9B9L8OjNLa7egn6QWLuz6Zaxye-xjbgVZ314WSGCSW_jWC6kaMUe14sJk4AApOXtRt6LvkVdHP3WVmCiVNOKFP6POy4myF4ZxbeLepx0Ot0KfIB1/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5419884466460831170" border="0" /><br /><img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiAdinB1csxvruME5UlE61sgUl-LOIKBpYYgWEC9eXwepMmf3I-O7RGSikWJo6gGBZvVdTz8MUTGgJejXjO1lUaKiUSUjSnaeAJ8eygBFuVHOP7qSU9UM5t2JzrEJHpfeByiw-d7D0POyG/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5419884454206474114" border="0" /><br /><br />Dengan demikian,<br /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9BIXfNrJB7h0Yyn4IrP-gMyea1IFKqd4yZOJ7iAj2gbxdaS5TwInKvyGPXmXlcdn8mqCesMQKB0xcq6a8WvaMdyu4H-WMo8g8nBqRMRZN6Sdnk2J5HenIy4fDSEv8HKd-GpdYpnRLzNha/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5419885292763267106" border="0" /><br /><img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1bcOnxSkkTRS0ag-8pOUBZFZ68Op91QwMZ9RIN5LsSb6qWGRbk1m7iIZFzW7-4-ywonFfp4lPm9x-Epahe9FWxQwSKEYwBsNtiljeljLvdWSHRxhhmVHihwmhhNPsEmj729kVcTG479Xj/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5419885287252793874" border="0" /><br /><img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgW7FZqOdEcLwO3NSLO7QPdha4pwpwMskEl9_L4Y5-CSSmuREZwcs7SylhqwHjUXjnuu6SPo0M72b2TsSsLWIguJKTKpViAW5AdAb82Sz9Iwygji2VDd1seslfexarJznRExA6ejNfK2O9L/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5419885624058665170" border="0" /><br /><br /><div style="text-align: justify;">Berdasarkan deret Taylor, <img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRCpzr9Cuc_UEKMn6RXbJCh_8y-RZfHXrVMMRt_Gjp0GgmAmkvxMyIe0AmMCZ_3JDCP3zSkaT3sWqaERjdTkRCjjLQQY_34aDyEkjB5yDiB9cqAO32WDM-b1zNbUWj_EAamCOWdpaTsnXT/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419887660858945954" border="0" />, maka untuk nilai n mendekati tak hingga: <img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWlWWJCaiYupEujRUs4PjYJ65-cdchYiEM-Oi3tGd9rf_HGwEahAlrSEVcnFu-cMOV0L2_u3p8ztgz6wmSRA5RMukLBkek-tcS2X9qvyO7_wDdvV438mQOXDSix4bGe6ew9LRB-ZyOiwoD/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419887663989484434" border="0" />. Artinya, peluangnya mendekati <img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgfoJQB8B8oJKzKke6-aNBauc8hNi1yCnjgiNbi4BIh_Dw6WKQFbDjj7QKBEC1xAzAiKMtHwKEoFw6r8w4XDunSwQnKfobI-eWsTE7JJxH8xeJHEkLlr586ggY8p1w-Lu-YrQtOgJLEAku/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419843115312057554" border="0" /> atau sekitar <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmlwA8G-qq-vpRmbIcYErYieCII86tKNjjDhnO9i_847Qge2ggegzkQ3yAfNYosOVK59o83vlWElBUPt-XgOxHeyTFFQ5RF5SiU5KpBs0o-JnMmZFiwfAY8w9w5wWnhFTBgGcPzEKpqEuM/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419843112767682338" border="0" />.<br />Namun, untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLhQltBSb08KyqI_EkAM95nYVfYSL3kHJaDbECPm0OjrmQ6C9awUcLEIdAyGiN2aF9u0BHag1ljD-NTZJjLAF_Hvre1E_iJMr8qX79EaPmtJKD4yoLy763weKqSfp7FeWAHIXMC7lVhRmp/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419888264649190738" border="0" />, nilai ini sudah didekati dengan baik, dan dapat kita anggap bahwa nilai n tidak memberikan pengaruh yang signifikan.<br /></div><br />=======================================================================<br /><div style="text-align: center; color: rgb(204, 0, 0);"><span style="font-size:130%;"><span style="font-weight: bold;">PENUTUP</span><br /></span></div><br /><div style="text-align: justify;">Penerapan prinsip eksklusi-inklusi yang lainnya masih banyak. Mungkin akan dijelaskan lain waktu di post yang berikutnya. :)<br /><br />So, kasus "<span style="background: rgb(101, 255, 80) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Matching Problem</span>" sudah kita pecahkan. Karena kemungkinan berhasilnya kecil, jangan coba-coba untuk menjawab ngasal ketika kita menjawab soal bertipe menjodohkan, karena peluang mendapatkan nilai nol adalah 40%. Wakakak.<br /><br />Ada yang kurang ngerti dengan pembahasan di atas? Sialakn ditanyakan di comment di bawah. :D<br /></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber:<br /><a href="http://www.math.hmc.edu/funfacts/ffiles/10001.4-6.shtml">http://www.math.hmc.edu/funfacts/ffiles/10001.4-6.shtml</a><br /><a href="http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle">http://en.wikipedia.org/wiki/Inclusion%E2%80%93exclusion_principle</a><br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com21tag:blogger.com,1999:blog-8125318493233557109.post-43863666767338459082009-12-25T19:52:00.009+07:002009-12-25T22:01:23.861+07:00Math Jokes<div style="border: 4px outset rgb(15, 50, 255); padding: 5px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Ada banyak sekali humor singkat tentang matematika. Langsung menuju TKP aja, gan. XD<br /><br /><div style="text-align: center; color: rgb(204, 0, 0);">1. Mengapa ahli matematika selalu kebingungan dalam membedakan Natal dan Halloween?<br /></div><div style="text-align: center;"><span style="color: rgb(204, 0, 0);">2. What's purple and commutative?</span><br /><span style="color: rgb(204, 0, 0);">3. Sebutkan 10 jenis tipe manusia yang ada di dunia!</span><br /><br />Jawab: (harus diblok)<br />1. <span style="color: rgb(255, 255, 255);">Karena 25 </span><sub style="color: rgb(255, 255, 255);">dec</sub><span style="color: rgb(255, 255, 255);"> = 31</span><sub style="color: rgb(255, 255, 255);">oct</sub>.<br /><span style="color: rgb(255, 255, 255);">Bilangan 25 dalam desimal adalah sama dengan bilangan 31 dalam oktal.</span><br />2. <span style="color: rgb(255, 255, 255);">Abelian grape.</span><br /><span style="color: rgb(255, 255, 255);">Abelian berarti komutatif.</span><br />3. <span style="color: rgb(255, 255, 255);">Mereka yang mengetahui binary dan yang tidak..</span><br /><span style="color: rgb(255, 255, 255);">10 dalam binary adalah 2 dalam desimal.</span><br /></div><br /><div style="text-align: justify;">Humor di atas kelihatannya garing, apalagi bagi yang gak tw istilah-istilah matematika. Huahuahua. Eit. Tunggu dulu. Humornya gak berhenti sampai di situ saja. Cekidot ni di bawah ini.. . Masih banyak yang perlu disimak.. Kalau bingung mengenai humornya, silakan blok penjelasan yang ada di bawahnya.. Maap kalo humornya dalam inggris, soalnya kebanyakan pake istilah inggris dan pengucapan inggris, tapi tentunya gak masalah kan bagi pembaca semua. Kan inggrisnya jago-jago.. XD. :)<br /></div></div><span class="fullpost"><br />=======================================================================<br /><span style="font-weight: bold; color: rgb(204, 0, 0);">Natural Logs</span><br />Q. Why do mathematicians like national parks?<br />A. Because of the natural logs.<br /><span style="color: rgb(255, 255, 255);">Natural logs adalah istilah logaritma natural, yang bisa juga dikatakan sebagai batang kayu yang alami (log = kayu).</span><br /><hr />Person 1: What's the integral of 1/cabin?<br />Person 2: A natural log cabin.<br />Person 1: No, a houseboat – you forgot to add the c!<br /><br /><span style="color: rgb(255, 255, 255);">Kita tahu bahwa integral 1/x adalah ln x. Maka, integral dari 1/ cabin adalah ln cabin (logaritma natural dari cabin). Namun, karena hasil dari integral tak tentu harus ditambahkan C (diucapkan seperti "sea"), maka cabin + sea = houseboat.</span><br /><br /><hr /><span style="font-weight: bold; color: rgb(204, 0, 0);">Mathematician and other professions</span><br />Several scientists were all posed the following question: "What is pi ?"<br />The engineer said: "It is approximately 3 and 1/7"<br />The physicist said: "It is 3.14159"<br />The mathematician thought a bit, and replied "It is equal to pi".<br />(A nutritionist: "Pie is a healthy and delicious dessert!" )<br /><span style="color: rgb(255, 255, 255);">Pi dibaca sama seperti "pie" dalam bahasa inggris.</span><br /><hr /><br /><div style="text-align: justify;">A physicist, a biologist and a mathematician are sitting in a street café watching people entering and leaving the house on the other side of the street. First they see two people entering the house. Time passes. After a while they notice three people leaving the house. The physicist says, "The measurement wasn't accurate." The biologist says, "They must have reproduced." The mathematician says, "If one more person enters the house then it will be empty."<br /></div><br /><hr /><div style="text-align: justify;">An analyst, a pure mathematician, and a statistician apply for a job. The interviewer asks each of them the question "What is 1/3 multiplied by 3?" The analyst enters it into his calculator and replies that the answer is 0.9999999. The pure mathematician replies that the answer is obviously 1. Then, the statistician asks the interviewer "What do you <i>want</i> it to be?"<br /></div><br /><hr /><div style="text-align: justify;">An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "How odd. Scottish sheep are black." "No, no, no!" says the physicist. "Only some Scottish sheep are black." The mathematician rolls his eyes at his companions' muddled thinking and says, "In Scotland, there is at least one sheep, at least one side of which looks black."<br /><br /><hr />An engineer, a physicist and a mathematician are staying in a hotel. The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trash can from his room with water and douses the fire. He goes back to bed. Later, the physicist wakes up and smells smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, etc. extinguishes the fire with the minimum amount of water and energy needed. Later, the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, "Ah, a solution exists!" and then goes back to bed.<br /><br /><hr />A mathematician, a physicist, an engineer went again to the races and laid their money down. Commiserating in the bar after the race, the engineer says, "I don't understand why I lost all my money. I measured all the horses and calculated their strength and mechanical advantage and figured out how fast they could run..."<br />The physicist interrupted him: "...but you didn't take individual variations into account. I did a statistical analysis of their previous performances and bet on the horses with the highest probability of winning..."<br />"...so if you're so hot why are you broke?" asked the engineer. But before the argument can grow, the mathematician takes out his pipe and they get a glimpse of his well-fattened wallet. Obviously here was a man who knows something about horses. They both demanded to know his secret.<br />"Well," he says, "first I assumed all the horses were identical and spherical..."<br /><br /><hr />A mathematician and a Wall street broker went to races. The broker suggested to bet $10,000 on a horse. The mathematician was sceptical, saying that he wanted first to understand the rules, to look on horses, etc. The broker whispered that he knew a secret algorithm for the success, but he could not convince the mathematician.<br />"You are too theoretical," he said and bet on a horse. Surely, that horse came first bringing him a lot of money. Triumphantly, he exclaimed:<br />"I told you, I knew the secret!"<br />"What is your secret?" the mathematician asked.<br />"It is rather easy. I have two kids, three and five year old. I sum up their ages and I bet on number nine."<br />"But, three and five is eight," the mathematician protested.<br />"I told you, you are too theoretical!" the broker replied, "Haven't I just shown experimentally, that my calculation is correct! 3+5=9!"<br /><br /><hr /><div style="text-align: justify;">Several scientists were all posed the following question: "What is 2 * 2 ?"<br /></div></div><div style="text-align: justify;">The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99".<br />The physicist consults his technical references, sets up the problem on his computer, and announces "it lies between 3.98 and 4.02".<br />The mathematician cogitates for a while, then announces: "I don't know what the answer is, but I can tell you, an answer exists!".<br />Philosopher smiles: "But what do you mean by 2 * 2 ?"<br />Logician replies: "Please define 2 * 2 more precisely."<br />The sociologist: "I don't know, but is was nice talking about it".<br />Behavioral Ecologist: "A polygamous mating system".<br />Medical Student : "4" All others looking astonished : "How did you know ??" Medical Student : :I memorized it."<br /></div><br /><hr /><div style="text-align: justify;">A physicist, a mathematician, and a mystic were asked to name the greatest invention of all time. The physicist chose the fire, which gave humanity the power over matter. The mathematician chose the alphabet, which gave humanity power over symbols. The mystic chose the thermos bottle.<br />"Why a thermos bottle?" the others asked. <br />"Because the thermos keeps hot liquids hot in winter and cold liquids cold in summer."<br />"Yes -- so what?"<br />"Think about it." said the mystic reverently. That little bottle -- how does it *know*?"<br /></div><br /><hr /><div style="text-align: justify;">A mathematician, a physicist, and an engineer are all given identical rubber balls and told to find the volume. They are given anything they want to measure it, and have all the time they need. The mathematician pulls out a measuring tape and records the circumference. He then divides by two times pi to get the radius, cubes that, multiplies by pi again, and then multiplies by four-thirds and thereby calculates the volume. The physicist gets a bucket of water, places 1.00000 gallons of water in the bucket, drops in the ball, and measures the displacement to six significant figures. And the engineer? He writes down the serial number of the ball, and looks it up.<br /></div><br /><hr /><div style="text-align: justify;">One day a farmer called up an engineer, a physicist, and a mathematician and asked them to fence of the largest possible area with the least amount of fence.<br />The engineer made the fence in a circle and proclaimed that he had the most efficient design.<br />The physicist made a long, straight line and proclaimed "We can assume the length is infinite..." and pointed out that fencing off half of the Earth was certainly a more efficient way to do it.<br />The Mathematician just laughed at them. He built a tiny fence around himself and said "I declare myself to be on the outside."<br /></div><br /><hr /><div style="text-align: justify;">A mathematician organizes a lottery in which the prize is an infinite amount of money. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment: "1 dollar now, 1/2 dollar next week, 1/3 dollar the week after that..."<br /><br /></div><hr /><span style="font-weight: bold; color: rgb(204, 0, 0);">Top Ten Excuses for Not Doing Homework</span><br />1. I accidentally divided by zero and my paper burst into flames.<br />2. Isaac Newton's birthday.<br />3. I could only get arbitrarily close to my textbook. I couldn't actually reach it.<br />4. I have the proof, but there isn't room to write it in this margin.<br />5. I was watching the World Series and got tied up trying to prove that it converged.<br />6. I have a solar powered calculator and it was cloudy.<br />7. I locked the paper in my trunk but a four-dimensional dog got in and ate it.<br />8. I couldn't figure out whether i am the square of negative one or i is the square root of negative one.<br />9. I took time out to snack on a doughnut and a cup of coffee.<br />10. I spent the rest of the night trying to figure which one to dunk.<br /><br />+ I could have sworn I put the homework inside a Klein bottle, but this morning I couldn't find it.<br /><br /><hr /><span style="font-weight: bold; color: rgb(204, 0, 0);">Weird Math Answers</span><br />Premise I: Knowledge is power.<br />Premise II: Power corrupts.<br />Conclusion: Therefore, knowledge corrupts.<br /><br />Premise I: Nobody's perfect<br />Premise II: I am nobody<br />Conclusion: So, I'm perfect!!<br /><br />Q: Why is 6 afraid of 7?<br />A: Because 7 8 9. (a pun on "7 ate 9")<br /><br /><hr /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikf2lorc6EQaDyP3Pz-aa_qp1oO0oxV6SsnullLPWy9Y0Nz169wm5hXCzbobX9cP9Fn8Nrkj0BU3JBFojvAp-6Q22uPA29NASTEIxETO-wvzPlIIWuxo_o-ZITLp2OK9em5MH9mW-HCotR/s1600-h/4.png"><img style="cursor: pointer; width: 343px; height: 43px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikf2lorc6EQaDyP3Pz-aa_qp1oO0oxV6SsnullLPWy9Y0Nz169wm5hXCzbobX9cP9Fn8Nrkj0BU3JBFojvAp-6Q22uPA29NASTEIxETO-wvzPlIIWuxo_o-ZITLp2OK9em5MH9mW-HCotR/s400/4.png" alt="" id="BLOGGER_PHOTO_ID_5419174867281122482" border="0" /></a><br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzmuJ71s27HyQKrKbLDijgvbFiseLOMcVUKr2VDNl6h2E9SH1CI7AzAnW18zOSQJ1-nZQijiGRW3fCb9TUvf2cOFp7RhzJHpewNbFGQNrzbqAqbKYikPT2jJMP8ZFrEYIZIC_Olh6YRjFH/s1600-h/5.png"><img style="cursor: pointer; width: 134px; height: 43px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzmuJ71s27HyQKrKbLDijgvbFiseLOMcVUKr2VDNl6h2E9SH1CI7AzAnW18zOSQJ1-nZQijiGRW3fCb9TUvf2cOFp7RhzJHpewNbFGQNrzbqAqbKYikPT2jJMP8ZFrEYIZIC_Olh6YRjFH/s400/5.png" alt="" id="BLOGGER_PHOTO_ID_5419174862939663570" border="0" /></a><br /><br /><hr /><span style="font-weight: bold; color: rgb(204, 0, 0);">Here is proof that women = evil:</span><br /><table><tbody><tr><td>Women are the product of time and money<i>:</i></td> <td><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMr7R6oCyQKN8wqtETDXB84r3z0SH3jwH7_TbSeCBnBAUgoY9qAXqe8FV_EB4zrCkelpclf8o2_GlXZ1ZS5bgxSoRBWKIOqBsXHAC3E6GaPGhNwfgxzyMeMQ3AlmGNhng0_SxgJkwXeuaU/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5419174359541734722" border="0" /></td> </tr> <tr> <td>Time is money:</td> <td><span class="texhtml">time = money</span></td> </tr> <tr> <td>So women are money squared</td> <td><span class="texhtml">women = money<sup>2</sup></span></td> </tr> <tr> <td>Money is the root of all evil:</td> <td><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDF2FcKH_VzQPTCENUYKF1U2w4xNK3b0wXgOIfdVYozRwVaGHtuHa08t0gEjxMkzJUoPJjHqDg-fnOOu-eKa_UtstbPzdXaPqVe0nmdDByqGtaJH8PZgWK_pmt7Aj5u_fUpkluBkQ9M0Fg/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5419174355389843218" border="0" /></td> </tr> <tr> <td>So women are absolutely evil:</td> <td><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivIBH_qjLnx2l1CZ7AiswSH9jlPfUz_dPsqxjrTsS-fAC25hZLybzMTtCHnTV-Bb25qiukRR6nud53w4i6WcAghEf4wasyVy9J-_qXu5BzzwHu78n-MEWFXl06QFrEg8xCGVyC2psEU6iB/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5419174352799470050" border="0" /></td></tr></tbody></table><br /><hr /><span style="font-weight: bold; color: rgb(204, 0, 0);">Salary Theorem</span><br />Postulate 1: Knowledge is Power.<br />Postulate 2: Time is Money.<br /><br />As every engineer knows:<br /><div style="text-align: center;">Power = Work / Time<br /></div>And since Knowledge = Power and Time = Money<br />It is therefore true that =<br /><div style="text-align: center;">Knowledge = Work / Money .<br /></div>Solving for Money, we get:<br /><div style="text-align: center;">Money = Work / Knowledge.<br /><br /></div>Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.<br /><br />=======================================================================<br /><div style="text-align: justify;">Sebetulnya, masih banyak lelucon matematika *konyol* lainnya. Yang ditulis di sini hanya sebagian kecil saja... Untuk lebih lengkapnya, lihat aja sumber-sumber di bawah. Bacanya pelan-pelan aja, sebagai pengantar tidur, dijamin 1 tahun gak bakal habis. Wakakak. :)<br /></div><br />Btw, lelucon mana yang paling lucu bagi kalian? XD<br /><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);"> <span style="font-weight: bold;"><span style="text-decoration: underline;">Referensi bagus:</span></span><span style="text-decoration: underline;"><br /></span><a href="http://en.wikipedia.org/wiki/Mathematical_joke">http://en.wikipedia.org/wiki/Mathematical_joke</a><br /><a href="http://www.math.ualberta.ca/%7Erunde/jokes.html">http://www.math.ualberta.ca/~runde/jokes.html</a><br /><a href="http://www.math.utah.edu/%7Echerk/mathjokes.html">http://www.math.utah.edu/~cherk/mathjokes.html</a><br /><a href="http://www.ahajokes.com/">http://www.ahajokes.com</a><br /><br /><span style="font-weight: bold;">Komik:</span><br /><a href="http://spikedmath.com/">http://spikedmath.com/</a><br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com25tag:blogger.com,1999:blog-8125318493233557109.post-43411115232312414382009-12-25T11:56:00.009+07:002009-12-25T12:54:06.591+07:00Funny Math Exams<div style="border-style: dashed; border-color: rgb(255, 0, 0) rgb(0, 255, 0) rgb(255, 155, 0) rgb(0, 0, 255); border-width: 3px; padding: 5px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Ulangan matematika selalu jadi momok yang mengerikan.<br /><br />Pernahkah kalian mengerjakan soal matematika yang benar-benar tidak bisa kalian jawab sama sekali alias <span style="font-style: italic;">ngeblank</span>.?? Di post ini akan dijelaskan tips dan trik menjawab soal-soal matematika tersebut dengan berbagai cara dan menggunakan kreativitas. Dijamin, guru matematika kalian "terpana" melihat jawaban kalian. (Note: jangan ditiru. lol)<br /><br />Di post ini akan diberikan beberapa contoh ulangan matematika yang "aneh" dan bikin kalian ngakak. Cekidot aja deh. <img class="emoticon" src="http://i298.photobucket.com/albums/mm247/erlia_onionhead/oh15.gif" alt="yay" title="yay" height="" width="" />...</div><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPuYf2Vi1WjZ9WgyhUhMbMNzJXqFpXeQheBgZIwfntb2C-RNcYcgsuWwOd91N3ZTIA1vmNVglyJRm-2suHDFrhhCGRGEXGbsEGw44Xb1TAx5xFb6j1JpZ44NQqNtHSpXdlccM3qKHLHlTb/s1600-h/title.jpg"><img style="cursor: pointer; width: 330px; height: 32px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPuYf2Vi1WjZ9WgyhUhMbMNzJXqFpXeQheBgZIwfntb2C-RNcYcgsuWwOd91N3ZTIA1vmNVglyJRm-2suHDFrhhCGRGEXGbsEGw44Xb1TAx5xFb6j1JpZ44NQqNtHSpXdlccM3qKHLHlTb/s400/title.jpg" alt="" id="BLOGGER_PHOTO_ID_5419037759444414226" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(255, 0, 0);">1. Nice Example. !!</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidLAIYx5uveK6eRd-hTiBXZSh9bz_BWs-N01LijHGxoj0ZHstn95ws0xCI6RYCQtCE5sMUUtGVrLYs9Uig_pcyozjFq3MZagLj9tmDZzC8DoYHlEUsgfY7RRi1e6EY_jL3x0TG86Y0txXA/s1600-h/01.jpg"><img style="cursor: pointer; width: 282px; height: 208px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidLAIYx5uveK6eRd-hTiBXZSh9bz_BWs-N01LijHGxoj0ZHstn95ws0xCI6RYCQtCE5sMUUtGVrLYs9Uig_pcyozjFq3MZagLj9tmDZzC8DoYHlEUsgfY7RRi1e6EY_jL3x0TG86Y0txXA/s800/01.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039914603011362" border="0" /></a><br /></div><span style="font-weight: bold; color: rgb(0, 153, 0);">2. Anybody could move that elephant there??!</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfuhL56aJlSROULpE1b8XHekg5Lgvk1l-Z2bpYo7Er9EL8QFggg75LnRS40DjTrJOvCGVP3XWIdbpAQfS04Nf_gsnYjs-2ypdTdngIrTjIAutVYcqVjp5lrnLms0pSt93rCYPvcTATfPZC/s1600-h/07.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfuhL56aJlSROULpE1b8XHekg5Lgvk1l-Z2bpYo7Er9EL8QFggg75LnRS40DjTrJOvCGVP3XWIdbpAQfS04Nf_gsnYjs-2ypdTdngIrTjIAutVYcqVjp5lrnLms0pSt93rCYPvcTATfPZC/s800/07.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039901976951442" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(51, 51, 255);">3. Technically right, but never again.. </span> <img class="emoticon" src="http://i298.photobucket.com/albums/mm247/erlia_onionhead/oh23.gif" alt="aargh" title="aargh" height="" width="" /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5iTYOjS42Vgx28nzId1KTkdnsH2jl4d0RqoKsNj32ir3NSoSf0NK99VM7b5tWFen6lLQFYN1EpLHLosJSCw_7i6JY3SsnEsQIpsk4T3l5HLobaadc5OWpfaNomwtJLr3QHO5lG5Jbu3rY/s1600-h/collegehumor_pic.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5iTYOjS42Vgx28nzId1KTkdnsH2jl4d0RqoKsNj32ir3NSoSf0NK99VM7b5tWFen6lLQFYN1EpLHLosJSCw_7i6JY3SsnEsQIpsk4T3l5HLobaadc5OWpfaNomwtJLr3QHO5lG5Jbu3rY/s800/collegehumor_pic.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039899105298162" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(255, 102, 0);">4. Nice description... ==..==</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5PO0KU2ALX7wZyIhgt2VvSv7iZCHRs9SqtNarKeH__vZLU8nh3t8Hed8elvR-Me9SXqo8-_OoMfCIAIaBnVLku98Gfiq5ysm12HiLOaE5TAbXtTgpuYPuuA5yW-vStRJg19LepFGOW8FM/s1600-h/curvygraph.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5PO0KU2ALX7wZyIhgt2VvSv7iZCHRs9SqtNarKeH__vZLU8nh3t8Hed8elvR-Me9SXqo8-_OoMfCIAIaBnVLku98Gfiq5ysm12HiLOaE5TAbXtTgpuYPuuA5yW-vStRJg19LepFGOW8FM/s800/curvygraph.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039645426075538" border="0" /></a><br /></div><span style="font-weight: bold; color: rgb(255, 0, 0);">5. It has been expanded, sir... I'm sure...</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Bk9WiyMcdVpQL3vhMPq_Cu5WeW006UFB1-xJrXa4j7wNTvAOXWqiRLuYvBYUtd4YM_8uNDi4tV3BVKgecWGDrz2f1KZ-O_btvK2jwXEQAwo-6py2XWcKZQEVMOfSOzi9hLdP65ZI0YQU/s1600-h/expand.jpg"><img style="cursor: pointer; width: 309px; height: 283px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3Bk9WiyMcdVpQL3vhMPq_Cu5WeW006UFB1-xJrXa4j7wNTvAOXWqiRLuYvBYUtd4YM_8uNDi4tV3BVKgecWGDrz2f1KZ-O_btvK2jwXEQAwo-6py2XWcKZQEVMOfSOzi9hLdP65ZI0YQU/s800/expand.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039636126970162" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(0, 153, 0);">6. Should think twice if using armadillo..</span><br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN6azE7fWxut3B4Mr0dcx1kawWrkV2PUQKU2JY_mdm2ESKIWktJJcn_PUvlIuT6UgZvebX95wIYAmmXs3I_NeBoB-SH2DkUcDvuFK1-VH4yzia7ER4VQ_YVruNH1FDiWNrIniCjHuGdW8e/s1600-h/Funny_test.jpg"><img style="cursor: pointer; width: 525px; height: 433px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhN6azE7fWxut3B4Mr0dcx1kawWrkV2PUQKU2JY_mdm2ESKIWktJJcn_PUvlIuT6UgZvebX95wIYAmmXs3I_NeBoB-SH2DkUcDvuFK1-VH4yzia7ER4VQ_YVruNH1FDiWNrIniCjHuGdW8e/s800/Funny_test.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039623535769554" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(51, 102, 255);">7. Hangman...</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0sLg55q2nC_Y_iGdfcZnz6nAcvyHJbqzdD9ZbRiuHwftof1SlteMNk8SrgAz8HapiMa_xzKkR9VowTmXrLtnNiAf33wFy_iGoiGaenX7f8Jg9p8yJoTxCP4YpFULsQJYlkcuAbfoEzks3/s1600-h/Hangman.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0sLg55q2nC_Y_iGdfcZnz6nAcvyHJbqzdD9ZbRiuHwftof1SlteMNk8SrgAz8HapiMa_xzKkR9VowTmXrLtnNiAf33wFy_iGoiGaenX7f8Jg9p8yJoTxCP4YpFULsQJYlkcuAbfoEzks3/s800/Hangman.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039614848905074" border="0" /></a><br /></div><span style="font-weight: bold; color: rgb(255, 0, 0);">8. Should have trained that elephant!!</span><br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyDUAUuJTaCmqYqyRqidJjdfSP7rd3XeS9o7VjW9lTlhoboToHPm5m_gUDoMYiuw34Afd_O1G_9TUpqYWHMNZSYGEUWlX2Ro7NHK6KxepWbMGNw2abjKgTwIQ-ji7nmCxM6CxF137NNsRe/s1600-h/PIC_0151.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyDUAUuJTaCmqYqyRqidJjdfSP7rd3XeS9o7VjW9lTlhoboToHPm5m_gUDoMYiuw34Afd_O1G_9TUpqYWHMNZSYGEUWlX2Ro7NHK6KxepWbMGNw2abjKgTwIQ-ji7nmCxM6CxF137NNsRe/s800/PIC_0151.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039237344803506" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(255, 102, 0);">9. Give up, sir. My picture is good, please give some values..</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj48fMZzXq6QDrPxS8uQZgYt8FHK-XJvxpEWANPn75xAgBG-v3TqFkeYhMHfCyMDI7rp4qhyVMX48lfcTpV22gCgxMzYIHQflPZTT2ufsHCKErqIqorBnVLdB3xWJDOFD_hBYBCnOSR42U-/s1600-h/Imagen2.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj48fMZzXq6QDrPxS8uQZgYt8FHK-XJvxpEWANPn75xAgBG-v3TqFkeYhMHfCyMDI7rp4qhyVMX48lfcTpV22gCgxMzYIHQflPZTT2ufsHCKErqIqorBnVLdB3xWJDOFD_hBYBCnOSR42U-/s800/Imagen2.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039268736369234" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(0, 153, 0);">10. I never think math exam is easy like this.</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4pjgWaHRz5ZW0FTCmoXJXPaqYX4fPitAgBz9RLtImhHUQRhrVzLJ_a9WRZwtoquWc74vwucoPNTS4WLNuhEEtn-vZitg9oR1mtE2ZEtua_mUPMMiHOQwicQLe3vOenSx4MUH097fnvGKi/s1600-h/PIC_0150REDUEX.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4pjgWaHRz5ZW0FTCmoXJXPaqYX4fPitAgBz9RLtImhHUQRhrVzLJ_a9WRZwtoquWc74vwucoPNTS4WLNuhEEtn-vZitg9oR1mtE2ZEtua_mUPMMiHOQwicQLe3vOenSx4MUH097fnvGKi/s800/PIC_0150REDUEX.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039240834093426" border="0" /></a><br /></div> <span style="font-weight: bold; color: rgb(51, 51, 255);">11. literally correct.</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEMkzx2ld2CesbUlDXdiEGaVxGHvAiT7GDGGhGzMvAtVZ7627KVUZsQe0Be_PIEaChjww1o6guTOenL0LL0Njxzuj9p1C_E9cV1JLoXqkNqZ6iJ5Kr-b5Lc7nddhSivJzJR1Zn2ry_Xpht/s1600-h/Picture_002.jpg"><img style="cursor: pointer; width: 361px; height: 120px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEMkzx2ld2CesbUlDXdiEGaVxGHvAiT7GDGGhGzMvAtVZ7627KVUZsQe0Be_PIEaChjww1o6guTOenL0LL0Njxzuj9p1C_E9cV1JLoXqkNqZ6iJ5Kr-b5Lc7nddhSivJzJR1Zn2ry_Xpht/s800/Picture_002.jpg" alt="" id="BLOGGER_PHOTO_ID_5419038971784731042" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(255, 0, 0);">12. Batman integral formula. Nice try..</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRHQogK7XUV3aaHmFRC21kl6ndpzDyox1amvbEj10_kG_nOLC1xyvyU3LWqSKBToEyguw7iRgTYobiHxMMY16jNlBFsv0LDZkFyIHUKJigqTd03yd7F7SCSzTDT1siUwJDMGsfdNEvmEYf/s1600-h/proton.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRHQogK7XUV3aaHmFRC21kl6ndpzDyox1amvbEj10_kG_nOLC1xyvyU3LWqSKBToEyguw7iRgTYobiHxMMY16jNlBFsv0LDZkFyIHUKJigqTd03yd7F7SCSzTDT1siUwJDMGsfdNEvmEYf/s800/proton.jpg" alt="" id="BLOGGER_PHOTO_ID_5419038964014786386" border="0" /></a><br /></div><br /><span style="font-weight: bold; color: rgb(255, 102, 0);">13. I'm hungry, sir</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi25EswwXRj5exPZ3cMF16lwuaOzFjF5Bi4HQZJS0m2_0CvCoK2OOKba0YI_7TiXAh83EiJTO0mJQ-yu3T9-PwkVRxYK-UrG9KEd8GtyDXsYfD-V9NK3YgxwD9qbPxlTB3a0Y5IPp44Dbvy/s1600-h/sushi.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi25EswwXRj5exPZ3cMF16lwuaOzFjF5Bi4HQZJS0m2_0CvCoK2OOKba0YI_7TiXAh83EiJTO0mJQ-yu3T9-PwkVRxYK-UrG9KEd8GtyDXsYfD-V9NK3YgxwD9qbPxlTB3a0Y5IPp44Dbvy/s800/sushi.jpg" alt="" id="BLOGGER_PHOTO_ID_5419038943790245394" border="0" /></a><br /></div><span style="font-weight: bold; color: rgb(255, 102, 0);">14. No comment.. ==..==</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX7NSxWokMUm6VknD_cmjxvMjOiFWV7OLYCyAiJ1Vpex5Jni0uXZqeMeQshaF7RigsCtsPUqs5juhsVPLr2ai2kcaZUHvSE9cIuMrXwIWeVea3Vixf2uuzBBn3wzFvuBvqsnsg3qKb15VH/s1600-h/sinx.png"><img style="cursor: pointer; width: 141px; height: 129px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX7NSxWokMUm6VknD_cmjxvMjOiFWV7OLYCyAiJ1Vpex5Jni0uXZqeMeQshaF7RigsCtsPUqs5juhsVPLr2ai2kcaZUHvSE9cIuMrXwIWeVea3Vixf2uuzBBn3wzFvuBvqsnsg3qKb15VH/s400/sinx.png" alt="" id="BLOGGER_PHOTO_ID_5419038956978004242" border="0" /></a> <a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcG8vLB1mewNRgPrQitzI7SgL4zNsdsYK2m7qyqPrK4SJG-XLurHgz0LSPsTCpn9UDyVqn2RLTPhNyMvNF1Kqnvj90NuZzimyMGz3wTyWKxZHb9uenkpDiQc0zDMyq8EV3dUlEv73wCVZX/s1600-h/sqrt2.gif"><img style="cursor: pointer; width: 95px; height: 85px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcG8vLB1mewNRgPrQitzI7SgL4zNsdsYK2m7qyqPrK4SJG-XLurHgz0LSPsTCpn9UDyVqn2RLTPhNyMvNF1Kqnvj90NuZzimyMGz3wTyWKxZHb9uenkpDiQc0zDMyq8EV3dUlEv73wCVZX/s400/sqrt2.gif" alt="" id="BLOGGER_PHOTO_ID_5419038955119457506" border="0" /></a><br /></div><span style="font-weight: bold; color: rgb(0, 153, 0);">15. Wow.. You really can find it.</span><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgImVCxlo5LE_TA8CZM16eB09R2146V9vjgcVhpoccrG_9w-PvipGYPvRtbOEFjcp0-tTyAZAgGHdN-6lSuD4eFUWwgmWiFsKcNtqXHelrURBtqGZIUu0pBHG9x7lJhbDEr9XbZD3WbRaVc/s1600-h/findx.gif"><img style="cursor: pointer; width: 214px; height: 150px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgImVCxlo5LE_TA8CZM16eB09R2146V9vjgcVhpoccrG_9w-PvipGYPvRtbOEFjcp0-tTyAZAgGHdN-6lSuD4eFUWwgmWiFsKcNtqXHelrURBtqGZIUu0pBHG9x7lJhbDEr9XbZD3WbRaVc/s400/findx.gif" alt="" id="BLOGGER_PHOTO_ID_5419039627863898818" border="0" /></a><br /><div style="text-align: left;"><span style="font-weight: bold; color: rgb(255, 0, 0);">16. This proof should be immediately published in the journal.!</span><br /></div></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkBq0foA0DMRx_be0dzNlwoe7WefPKFO8FSTTTMiiwdLNGOrjZ0b9xr2Cl2E6Yt525eKX38b1Sn6XXIdikCWUXwsZ-o5hBgUVR6AjCF3JgNdCcYY0LR6RLJZP7BqGTsAsfdg9OM8lQlhiz/s1600-h/02.jpg"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkBq0foA0DMRx_be0dzNlwoe7WefPKFO8FSTTTMiiwdLNGOrjZ0b9xr2Cl2E6Yt525eKX38b1Sn6XXIdikCWUXwsZ-o5hBgUVR6AjCF3JgNdCcYY0LR6RLJZP7BqGTsAsfdg9OM8lQlhiz/s800/02.jpg" alt="" id="BLOGGER_PHOTO_ID_5419039909858761954" border="0" /></a><br /></div><div style="text-align: justify;">Ini adalah jokes tentang ulangan-ulangan matematika yang aneh. (Beberapa nomor sebetulnya bukanlah ujian, tapi dimasukin juga). Ada lagi post berikutnya tentang humor matematika yang tidak mungkin digabung di sini.. :D.<br /><br />Jokes yang berhubungan dengan pelajaran lain, seperti bilogi, fisika, kimia, atau bahasa dapat dilihat di <a href="www.funnyexam.com">www.funnyexam.com</a>. Mantabz deh. Dijamin ngakak.. :)).<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com19tag:blogger.com,1999:blog-8125318493233557109.post-59498798990434973162009-12-20T21:59:00.007+07:002009-12-23T11:02:16.428+07:00Menghitung Volume Donat<div style="border: 4px dotted rgb(255, 201, 77); padding: 5px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Suatu hari, dalam perjalanan pulang, Grace merasa lapar. Untung saja di tengah perjalanan ada toko donat, maka Grace pun berniat membeli donat.<br /><br />Ada dua donat, donat A dan donat B, yang keduanya memiliki ukuran yang berbeda. Donat A memiliki rotinya lebih tipis dibanding donat B, namun memiliki diameter donat yang lebih besar dibanding donat B. Lebih jelasnya, lihat di gambar.<br /><div style="text-align: center;"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghgOc79uLrVEW1f4gh8WBCQaAn8d0HZzWC6AVRmC7n1NttBZ2baUpnbd-AWcpnPaX5DUmYYYMjSS12H_xb3YvdteXdkSTFACIvpaL0EmWBIT63S-sYl-V2PgRBmrDBobX08AShaqouSd5Z/s800/2donut.jpg" alt="" id="BLOGGER_PHOTO_ID_5417340436937480978" border="0" /><br /></div>Grace ingin donat yang volumenya lebih besar. Bisakah kalian membantu Grace menentukan donat tersebut? Jelaskan alasanmu!<br /></div><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center; font-weight: bold;">Penyelesaian<br /></div><br />Pappus' Centroid Theorem I mengatakan bahwa:<br /><div style="text-align: center;">Volume V yang dibentuk dari perputaran suatu figur F terhadap suatu sumbu eksternal<br /><br />sama dengan<br /><br />perkalian area (A) dari figur F dengan<br />panjang keliling lingkaran (jarak yang ditempuh oleh pusat massa selama diputar)<br /></div><br />Digambarkan sebagai berikut. (M adalah titik pusat massa.)<div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmCIz8xPewgjwgJ3rZBQRgCoMOqel9kCUKY8zEZiwaFnjOdo1yNjGV50r4PW79meQEfETiWlK2vRr1cSNV7ZjpVIrBGV5iDz6d1kf9mwqMPH0MuZuyW7XZ5LAiY4vqRvnQBZH4gProdNUj/s1600-h/pappus+II.jpg"><img style="cursor: pointer; width: 287px; height: 189px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmCIz8xPewgjwgJ3rZBQRgCoMOqel9kCUKY8zEZiwaFnjOdo1yNjGV50r4PW79meQEfETiWlK2vRr1cSNV7ZjpVIrBGV5iDz6d1kf9mwqMPH0MuZuyW7XZ5LAiY4vqRvnQBZH4gProdNUj/s400/pappus+II.jpg" alt="" id="BLOGGER_PHOTO_ID_5418272071400373282" border="0" /></a><br /></div><br /><div style="text-align: center;">Volume yang terbentuk dari perputaran = Luas A x 2. <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEJicCd6DnCbNv4EQZVY7-tJ627HVvR2BJtXD-xcEmz4fjs3BrU4EkC5eUd5ypQlg0JDY64HhFOrOtIFpPiu2ysQ4_EQX3YWDj5okU6kGJhaFXPr8lA71ZESQ36QSvAgtk_MLH-ocO9-eE/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5418274219736444514" border="0" />.d<br /><br /></div>Dengan demikian, kita dapat menyelesaikan kasus donat di atas dengan sangat mudah.<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK7pnflAzd8Qarw1Srzxr6FNLVuJNQorf_SSN2LQeP2J2Bao_xgGIrgbodqAmv4lBXHoGDXvDtb5LPOt06j1PUtTHPjQ6zFDmb_xEuN0EYgXqe0Lh5izeCehi5I4tUsqFhU_QeD84f2tGb/s1600-h/2.gif"><img style="cursor: pointer; width: 243px; height: 19px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhK7pnflAzd8Qarw1Srzxr6FNLVuJNQorf_SSN2LQeP2J2Bao_xgGIrgbodqAmv4lBXHoGDXvDtb5LPOt06j1PUtTHPjQ6zFDmb_xEuN0EYgXqe0Lh5izeCehi5I4tUsqFhU_QeD84f2tGb/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5418276200464466818" border="0" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidZwTtObiVevbf23gjHpWsgn7VZDxgXfeZW_SdKzSXQnoqCw4p0S5Atvg7_aZ4NH4R3izdkZarJyfSUxiGN1ViDiUFHeDjqrb3M1oDR7jLy1ZLxoLNGu4Iflt6xRSdaFi3GPrvNVRWkhMq/s1600-h/3.gif"><img style="cursor: pointer; width: 178px; height: 19px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidZwTtObiVevbf23gjHpWsgn7VZDxgXfeZW_SdKzSXQnoqCw4p0S5Atvg7_aZ4NH4R3izdkZarJyfSUxiGN1ViDiUFHeDjqrb3M1oDR7jLy1ZLxoLNGu4Iflt6xRSdaFi3GPrvNVRWkhMq/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5418276198350637410" border="0" /></a><br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiulw6uUZfEkpc3E_-oq7ZR-H1UEen3VTHaxN2DhvEv8j2TR6H5vYKma9FrjPDK73Vf-WBtFTK8GcSxr1xDwLs5zhJuyJH8bAspZdsMaacZ8qNrKD6wxTCkqD1heenIzrvIiPJpOmskDh2_/s1600-h/6.gif"><img style="cursor: pointer; width: 221px; height: 19px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiulw6uUZfEkpc3E_-oq7ZR-H1UEen3VTHaxN2DhvEv8j2TR6H5vYKma9FrjPDK73Vf-WBtFTK8GcSxr1xDwLs5zhJuyJH8bAspZdsMaacZ8qNrKD6wxTCkqD1heenIzrvIiPJpOmskDh2_/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5418276193305111570" border="0" /></a><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm2AkJ60knZxpcyaxSyiDpqo8Fpp7qX0rrm6VC3DPWleAA8xWtGffnDc_c5hY4MnpKa2xIrR6HCQ7YjFVQR5hy-ApV_zwmEVfd3Xe0FspR8ZLiaqlK7joya4pMo4EFke7XVDTUmThif4-o/s1600-h/5.gif"><img style="cursor: pointer; width: 146px; height: 16px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhm2AkJ60knZxpcyaxSyiDpqo8Fpp7qX0rrm6VC3DPWleAA8xWtGffnDc_c5hY4MnpKa2xIrR6HCQ7YjFVQR5hy-ApV_zwmEVfd3Xe0FspR8ZLiaqlK7joya4pMo4EFke7XVDTUmThif4-o/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5418276188314775602" border="0" /></a><br /><br />Jadi, jelaslah bahwa donat kedua memiliki volume lebih banyak dibanding donat 1.</span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com10tag:blogger.com,1999:blog-8125318493233557109.post-37698732120341339342009-11-22T21:55:00.007+07:002009-11-26T00:09:22.424+07:00Makanan Otak... (xxiii) Jika sisanya samaReza mempunyai sejumlah <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5nM_C0Y6PrLXnI7NIz8dhWHfSYJqjwlFLpsUIMBXy9JQYMO_XXsbwLgMGyXnt8B9Yc93atXaPLN08-B-ntJDwfYQGk0LwQm0qTsPWDdVIhs-72puxQbTXAPcAoLz0_cmShEEzy5rvIxpK/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5406943167158151090" border="0" /> motor.<br /><div style="text-align: center;">Jika <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5nM_C0Y6PrLXnI7NIz8dhWHfSYJqjwlFLpsUIMBXy9JQYMO_XXsbwLgMGyXnt8B9Yc93atXaPLN08-B-ntJDwfYQGk0LwQm0qTsPWDdVIhs-72puxQbTXAPcAoLz0_cmShEEzy5rvIxpK/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5406943167158151090" border="0" /> dibagi 8, maka akan bersisa 7.<br />Jika <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5nM_C0Y6PrLXnI7NIz8dhWHfSYJqjwlFLpsUIMBXy9JQYMO_XXsbwLgMGyXnt8B9Yc93atXaPLN08-B-ntJDwfYQGk0LwQm0qTsPWDdVIhs-72puxQbTXAPcAoLz0_cmShEEzy5rvIxpK/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5406943167158151090" border="0" /> dibagi 9 maka akan bersisa 7.<br />Jika <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5nM_C0Y6PrLXnI7NIz8dhWHfSYJqjwlFLpsUIMBXy9JQYMO_XXsbwLgMGyXnt8B9Yc93atXaPLN08-B-ntJDwfYQGk0LwQm0qTsPWDdVIhs-72puxQbTXAPcAoLz0_cmShEEzy5rvIxpK/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5406943167158151090" border="0" /> dibagi 12, maka akan bersisa 7.<br />Jika <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5nM_C0Y6PrLXnI7NIz8dhWHfSYJqjwlFLpsUIMBXy9JQYMO_XXsbwLgMGyXnt8B9Yc93atXaPLN08-B-ntJDwfYQGk0LwQm0qTsPWDdVIhs-72puxQbTXAPcAoLz0_cmShEEzy5rvIxpK/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5406943167158151090" border="0" /> dibagi 20, maka akan bersisa 7.<br />Jika <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5nM_C0Y6PrLXnI7NIz8dhWHfSYJqjwlFLpsUIMBXy9JQYMO_XXsbwLgMGyXnt8B9Yc93atXaPLN08-B-ntJDwfYQGk0LwQm0qTsPWDdVIhs-72puxQbTXAPcAoLz0_cmShEEzy5rvIxpK/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5406943167158151090" border="0" /> dibagi 25, maka juga akan bersisa 7.<br /></div><br />Yang pasti, jumlah motor si Reza bukan berjumlah 7. Jadi, berapakah jumlah motornya?<span class="fullpost"><br /><br />=======================================================================<br /><div style="text-align: center;"><span style="font-weight: bold;">PENYELESAIAN</span><br /></div><br />Di comment di bawah, jawaban sudah diberikan, yaitu 1807.<br /><br /><div style="text-align: justify;">Soal di atas sesungguhnya hanya mencari KPK dari 8, 19, 12, 20, dan 25, kemudian hasilnya ditambahkan dengan 7. Mengapa bisa demikian? Sebagai contoh, lihat 2 persamaan saja. Misalkan persamaan<br /></div><div style="text-align: center;">Jika <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5nM_C0Y6PrLXnI7NIz8dhWHfSYJqjwlFLpsUIMBXy9JQYMO_XXsbwLgMGyXnt8B9Yc93atXaPLN08-B-ntJDwfYQGk0LwQm0qTsPWDdVIhs-72puxQbTXAPcAoLz0_cmShEEzy5rvIxpK/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5406943167158151090" border="0" /> dibagi 12, maka akan bersisa 7 ... (i)<br />Jika <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5nM_C0Y6PrLXnI7NIz8dhWHfSYJqjwlFLpsUIMBXy9JQYMO_XXsbwLgMGyXnt8B9Yc93atXaPLN08-B-ntJDwfYQGk0LwQm0qTsPWDdVIhs-72puxQbTXAPcAoLz0_cmShEEzy5rvIxpK/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5406943167158151090" border="0" /> dibagi 20, maka akan bersisa 7 ... (ii)<br /></div>Dari (i) kita dapatkan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJoVPMXFcri_9yjx-tqdh2lxy_Ynq_RIpmh5dULTdY3eUz7uWGn8fcitSknFF0_uLQm_XqHGBgLT-9VANAOVvRjByEXTyiFr_QKEbOsnQP_ktf1tXlW03nv6qbQSHXluuQu4SgcZzryHgq/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5408079302507297474" border="0" />, maka <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhA_NzQC4uFO4ycoRHVavuPgSd0QQBLHeo02UZ2BJro7cGhDh-bnlo0OE_mexfwM4ZtsNjNBFt_CTwa4XDAMjMwQWBC-fK-QF7eGtkD7N22N3ER91u2JCm9_boWAjKyG2iEqY_pq_Axyq7u/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5408079292290768642" border="0" /><br />Dari (ii) kita dapatkan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj__wp4xkaVWSJC00-6SPdfzid7eWdxZ9QVfEvVMwqWXM5bPX6Gx6e9Ha2mQpC7F1jd8bDq2tZs0Z0pQzg0j7PT131QPrer28k5o9fklweuFQsu49cnzk2y42uE0Oo2nVM2m4bNpc3QKeYa/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5408079298031649058" border="0" />, maka <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1PI8kM5anQQf_z7S1Gh4BV-MEC0n6d7Q6HqaR1FZp_hPKNjKqQkOngu9xZwbElWDHCcEbg4hBkE6ctnL7Xobpq_rrv7Wcim_6JFeXI8aRC3XAXSuFKxqvPEL1kjMyB83l92Cwnqi0Qq5e/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5408079481954773858" border="0" />.<br />Substitusikan (i) dan (ii), maka<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3CYsb7InMH7txo-berTbcZokJIyJJ4mpmzhyphenhyphen1mJwObasvR7sNr2nUD86iqyEIamEcPNKnk8-hnOq40H8vj-K_bUHnFlB_l_8R-cqHPbiFxbZOkactZ-Xo2ueoiMTlzwEHuaCyNt2IPFJ5/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5408081392784849186" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjHiQ09aiQ0UZL3DegCp9ipRG-w987PTqEO_nbymwl3UFSItRrm6DWkj6HcGqUoHIXxaXe1PO4-OVH10eC1pkDSoaodo45m2JSpJJb7XPn7XTmJNK0GP1gLNyawdHzBKb1SBDSwkUkbo1l/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5408081382949229938" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8eK7Wx30RyOycxXKopu9aQNBF1n6l0usxCwDzGNJ2vwzBxVnRIY03LJIXhgV83wqLu5iTNg7JQO4Cr-4Nh4nbnXYiW_w4__Wb2y5e0JnzZWxGjsSkWH-kb9t95Vw-m4eHrvQ7DITjGWTw/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5408081378992617330" border="0" /><br /><div style="text-align: justify;">Karena ruas kanan kelipatan 5, maka ruas kiri juga harus kelipatan 5. Maka nikai k harus kelipatan 5.<br /></div><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBFsw5blsguPNPe2G7S_ImbOlZuV0E9a-eFglLXslSfeNIxokrdGRRUh_A1bOo_QKiPB7Tszy-wTYKcYQZqn6D9WJv3aX7f5vmOrKVFJyNm7YckweFW_-mopjOThphLiWz5BnT7j3NZy39/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5408083092248013986" border="0" /><br /></div>Substitusikan k ke (i)<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyzBg6P5obnUxtPB30j8VSltVFLfCpbchmbZ6do_Ky907MLB0UUsfi8RqTzi8jZv6iia8Hp_7RWKce6zePJZdcJPJ_HkmAHCDwDX1JfMFMrwXZg1hg6cXF6rOxuKp7jNXOx98_r4WZCYGQ/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5408083943355560050" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKCVZCStNIOYlu-5J47xEXPUggWjS2MxYLlXUh47d_T0SE-BdKWvVEC1t815FSiJMLF4i9wTihloKG0VHpI2UxK6Zz1MsX9uErB5C4HNSZQxE0Ja_ZqnHUiSXlQJaoPCIcMDLiJpNz6py1/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5408083940865317826" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivxPnYnMNCCCXEF1tj8q06F-IPMa5BcVvVAHTLOQt3I9IpPwl-7VwubvsHzB8M67M6L3b3r7FppZiVjEnBWrIPz3BAjD5oypsYZNQO1JN4JzRbDA2ML4J3yjfklZs1Dl8y5mNuQ1BLWixY/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5408083934906893346" border="0" /><br /></div><div style="text-align: center;">Ini adalah penggabungan syarat (i) dan (ii)<br /></div><br /><div style="border-style: dashed; border-width: 1px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Perhatikan langkah-langkah di atas. Sesungguhnya nilai x sama seperti rumusan di bawah:<br /><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4OfNK9OdfQSgz_xfzvCNC3OW9v2Q4mV52VZ4DU8Wkoo_IhNJkhilJvZMlzh6_FWLKu6NwTj_Jtx67m0bXgc_94lcwykPyfI3xnK62MmlIdnxuBkAZRb1-rbZHE3ijPiYV5x9H5iJPSxyH/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5408085041919875778" border="0" /><br /></div>atau dapat ditulis:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUC0uLgJeycjScqKNNFS9RoUeweaEhjcSeVPH88soNwXj73CYIGObHD2LbHfUIlUMrxckJPu21_Zqjox9WfIXp4FKRq8IRfeDiDvYw_Dw5epqgI9feuv8T67e_xT_Ho5zNZS2wWfw74BRp/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5408085033557884450" border="0" /><br /></div>lcm (least common multiple) disebut juga KPK (Kelipatan Persekutuan terkecil).</div><br />Jadi, untuk menjawab soal di atas, jawabannya adalah:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVnxjNxyLcFqmti94K_P8-SbQiXxfhlgQ1m_DCU_D5JuNQTwOXJs8xJFRwfMDeaeanoTHxOV5Zv4cKHQlB5mYvHlYUEZNgMvjGUDtg4g_p008NCjd5g5j7r55K0qCCf9Jts7XNY6eSpc9t/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5408087693931780946" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSxNhA8iROuqUCV1YoapnxXAd4zkATktC0ahC53WWlWwzca7-chlXZ3zra-hjqoyBMmdzlsESYsIjpTQYDRZnRsIer2UWuQQthkf5h0C8hn-sxMsm99VIAIvAAoHgtq3969vKrCiQX8DEp/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5408087688581459922" border="0" /><br /></div>Karena, x bukan 7, maka kemungkinan adalah 1807, 3607, atau seterusnya.<br /></span><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Note: Nama disamarkan, karena si pemilik nama merasa malu.. Wakaka </div>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com12tag:blogger.com,1999:blog-8125318493233557109.post-36703992072490835212009-11-13T08:12:00.011+07:002009-11-13T20:32:30.257+07:00Makanan Otak... (xxii) Carilah x^4+y^4+z^4Mungkin, kalian pernah menemukan soal seperti ini di buku SMA:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifOO4DWfzz30pUQcD5EUUJ2boR3AqK3tlVY7d7pAthCxomwgR5kam9Qs09JDqQQeYbf3-yFPlOYf7VsV8Vld4Q2SUF5YJW9GhVq2vOYqlfDLH_JKIn2i-GtxTzt_ZzBNr3vBBe2K2sL6Ot/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5403391772945789106" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimWFFyhyphenhyphenn7DDXt5YWpfogc_VQ2FMXqR0HPCipLg95-JIkAQquFBF1OFABM3hshP3ZQCUCtQJ2A7SsLwmML2uVcLZDSi8Bp7Foi4XCOW_5bKHGaiAP3Jl7vnP8oQXOrJYrnBUzOXhqkOXvM/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5403566245577333874" border="0" /><br />Tentukan nilai <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxbtHLmCb5sR2PipMJL0PDMw38Amq9F3BY-_-tL6QlxlvCU4t3q0a-n6xoPa_LmJi3vgoECi6_U6gv06dYnIiLMNYxDZps3JvSyteHybyQIqq13lXFp4_asA9WwVA5wEHxinlDrA_gp8ll/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5403391692691535954" border="0" /><br /></div><br />Kali ini soal yang diajukan sedikit berbeda. Hanya menambahkan 1 variabel, yaitu sbb:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEha-E5M1Mb9eRIYYS4y-zM-ano8FisBgY-vlyLWJ8ChNWW7NiBOxn6yuAI_03-s5C5BjRGek5AZN8bwJEF1yVO6uw6urgMTrs7MuiWqhRP-AJXTOrPAwBK1cNc_6dRovcjwGdgdpVANuKM6/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5403391686500521858" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqwzrLsdyIgNUFvSNlr9LbP1zgHQw1JLCMStss5hmaZEXfz2aTMdB7CcoiFmWSso897UQ_-yVRu5cQHPL2R4_x9KsB8k-oCOnyYffZZNUg13aGIGAfZtkloGJA0ij6koGOa4Qwo7mY8Ef6/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5403391685045065058" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc2LLc211uByN44-1Mp0mFle2K-ovHwNZVqFkiusBXUR4miCPlb-PK97LRRvKoTXOD1Ha6B4_CIUBfVBIqjnbutbjk0n0RxZsOdRmlIizt5sb_DT0VVMSvqQQKvc2qcB4XrAzW38flWTmv/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5403391677630208370" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyRLWbA78qSqFCrqnTwfLpP-UrIp_Kb9BgQg1J6YeuMJrhRvAb_eV7mSW8I9ByaLTcVYwmFzcgMlJXtoY0V8cAtBatQfPNdswfwW9W2qvFnOadFU5exGMYKfsw7QFeZUolWpuaKZ89Tfee/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5403393347155027218" border="0" /><br />Tentukan nilai <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEGAS2kLAxMIxEfiCGVb5S-qk0_CMI5LCZvbik-7xBdtTxpKM9TtwPowDibf-BP9fGR7u780u2oB5mE8ThW5mzP7wjoWmaYabgzHO6QP2xxt98CGXjp0QIhptVN5zeAVHIA4BphMeVrUwY/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5403392354947535794" border="0" />.<br /></div><span class="fullpost">=======================================================================<br /><div style="text-align: center;"><span style="font-weight: bold;">PENYELESAIAN</span><br /></div><br /><div style="border: 3px dashed rgb(200, 104, 250); padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Untuk soal yang pertama:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifOO4DWfzz30pUQcD5EUUJ2boR3AqK3tlVY7d7pAthCxomwgR5kam9Qs09JDqQQeYbf3-yFPlOYf7VsV8Vld4Q2SUF5YJW9GhVq2vOYqlfDLH_JKIn2i-GtxTzt_ZzBNr3vBBe2K2sL6Ot/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5403391772945789106" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimWFFyhyphenhyphenn7DDXt5YWpfogc_VQ2FMXqR0HPCipLg95-JIkAQquFBF1OFABM3hshP3ZQCUCtQJ2A7SsLwmML2uVcLZDSi8Bp7Foi4XCOW_5bKHGaiAP3Jl7vnP8oQXOrJYrnBUzOXhqkOXvM/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5403566245577333874" border="0" /><br />Tentukan nilai <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxbtHLmCb5sR2PipMJL0PDMw38Amq9F3BY-_-tL6QlxlvCU4t3q0a-n6xoPa_LmJi3vgoECi6_U6gv06dYnIiLMNYxDZps3JvSyteHybyQIqq13lXFp4_asA9WwVA5wEHxinlDrA_gp8ll/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5403391692691535954" border="0" /><br /></div>Jawab:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhj5drgjM8CNhRe8-609khq8U9SY1FGM4t3EeNg26milSGSgK1IdnklPjdLn_NlG1qFlqlzu0zGtixIaAEYv6CTqVxHFYVTHyvZ4fS3qRAq4Rr93a4gzm6V1zq4K5WAHbPbcY0un6QsSYcZ/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5403567444509102562" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2Fmk8mvIIU_AtS1CaFQBGmiJz5WFYWqoVFlIVR8qsr7RBy2cdqYj8GzvIpBIRkZ0yVNQj3BrgNzLB6G0GW9SofF7R85dMf9uO-NLZ355ZosUd1HH3vsWwHRRHyAlfvTiBUhrnJQw116uz/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5403567439903594658" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJc8L8pl2NttAiBAIR2uA8lEliWq1aUZIxAUADlnSUgKF6IsdFBySFl8arKLbXwUODR9va6E6c073cDb3il7-FvozAud7pLgF5QquafaIEhKyHb7j8_JBz_u50VGo5sYdn-xEMzTP5MLVA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5403570149337189762" border="0" /><br /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqoxmhFVB0c0hTgU4nYXjXaJPSoRqArrGNmsqf8Q-LiacyhYcWiVqLCcw3L-aaoXsJHtnXAEmJSu2SNeACkcHcenSQ-hf7ovz-CP89z1OM9T2JHSgLYpLbziermsOU7yyoora116uGYIV1/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5403567154330039650" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLKn8kjOEd39fh8yQX1wntBFwjaP8zACZVO9h2Co3cp0l8iogbixZalmBEdO2GdHc66bcZ4qFeNcP6rbvZpwYFcNAwPJ45sE7YW3PNODpTWaUHBVEj8YarRuCLJ8aOBPhqKt43eIvpjDDU/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5403567151299283346" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiU4K-Qvxjud9esyabt8LHuoTPrapHmKKw3P2jBDMpQ5AAjuNHHPyCp3NIHwZJMYL_QNG2Y2-6v_5UT6S1e-1ctD5qDQ1ovffjD_M-ACejmC1zoAKt_3_UOMBt5SCrySMO4QxhkWEqR9a6o/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5403567151344050818" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWuu8-qam2_K1zjEdLaeuZAHRPCRD8I5u0FBOEGlbTqn8qi-EvjmVQEcJZ93VvEegTIXKWQihzo0Z_rldb4pRGkYAhJo4feImCStXRioBKeBnQZEE7DfhrasoJt2qZyoeGMsBIB_qkStxK/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5403567146343334386" border="0" /><br /></div></div><br />Jika konsep dua variabel sudah dipahami, maka untuk 3 variabel juga sama, namun sungguh lebih ribet... X(. Silakan lihat di bawah...<br /><br /><div style="border: 3px dashed rgb(100, 204, 250); padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Soal Kedua:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEha-E5M1Mb9eRIYYS4y-zM-ano8FisBgY-vlyLWJ8ChNWW7NiBOxn6yuAI_03-s5C5BjRGek5AZN8bwJEF1yVO6uw6urgMTrs7MuiWqhRP-AJXTOrPAwBK1cNc_6dRovcjwGdgdpVANuKM6/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5403391686500521858" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqwzrLsdyIgNUFvSNlr9LbP1zgHQw1JLCMStss5hmaZEXfz2aTMdB7CcoiFmWSso897UQ_-yVRu5cQHPL2R4_x9KsB8k-oCOnyYffZZNUg13aGIGAfZtkloGJA0ij6koGOa4Qwo7mY8Ef6/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5403391685045065058" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjc2LLc211uByN44-1Mp0mFle2K-ovHwNZVqFkiusBXUR4miCPlb-PK97LRRvKoTXOD1Ha6B4_CIUBfVBIqjnbutbjk0n0RxZsOdRmlIizt5sb_DT0VVMSvqQQKvc2qcB4XrAzW38flWTmv/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5403391677630208370" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyRLWbA78qSqFCrqnTwfLpP-UrIp_Kb9BgQg1J6YeuMJrhRvAb_eV7mSW8I9ByaLTcVYwmFzcgMlJXtoY0V8cAtBatQfPNdswfwW9W2qvFnOadFU5exGMYKfsw7QFeZUolWpuaKZ89Tfee/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5403393347155027218" border="0" /><br />Tentukan nilai <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEGAS2kLAxMIxEfiCGVb5S-qk0_CMI5LCZvbik-7xBdtTxpKM9TtwPowDibf-BP9fGR7u780u2oB5mE8ThW5mzP7wjoWmaYabgzHO6QP2xxt98CGXjp0QIhptVN5zeAVHIA4BphMeVrUwY/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5403392354947535794" border="0" />.<br /></div>Jawab:<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzXCFXAHAjE7fefXrlTO0OeoSsCyhhpRTi3GBrNEa9NsJ084muD65G6nP1pR0Jhin5KveqGEPNV9qx-mxxYlPwF0Ivq9QODSJFKGwx_P4JNdK2l_QtHi443EoQ3DM9QQ0WrVbTnp0XixX0/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5403571370743820498" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQ5VjlznrJwTZzn2UOu89Y-xVZfn4QKIF4GsxGujPUH0siOwl0QoUAl3hWtvA2Q81NCbWmtMUHtFGiLQj54j5qugf1tX8UQXxw2CdfQMADhLMG_3cIy2tZrafqKw7o0mlOmJ89n-xC0R_I/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5403571365321277618" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjx5cmmRVpTLKaXU7yoTzx0CdiiHczgrhR_7xHSLkeZ8vChpIEPLkljzaTMxNYNbmCJlyKF9YTEAI_aHGThggL07Z_B0x_kUmscsgsC4YGKJ6bBNYIFmccC2YGIdmY6L8gu9MiSMCVoC6lh/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5403571361572463810" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBFmdPUCIU43t2n8tMXjDCSnBFPL9LgfKk2ETb0Um305e4e7SVTRVF04YjTAsfyCuoIB16TasOdbcCZsbhsIbNqX1b9UUy4BbWzSEFSuwSpq3W7_MMsuS3dWVGAvEpL8gJiSK0BEk_GvDa/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5403571363277866338" border="0" /><br /><br /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3S07_zAP9KjIfmV3CLSX6OmrqgskwiMGyi6KuHAHhkpVmBzmj4rTUDbBPXdeCYKn_MnrIl3L-6xMV74Ddf_XiVpVTe9OkJnCtoYcAXOktFPLpYJ-EY8CBiqOceRVYLaww4-u8COMJQdDQ/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5403572257838808226" border="0" /><span style="color: rgb(255, 255, 255);"></span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn9oQm0PFrxvczJpiuE87KQVgOfiDUgISMkOQLeaygs295pc9Eouo9JnJL9QLlCJeByrLSh06B1ynKqCiHCM2SrFfUWq_P47p3yjp9gT9OY-lDBg9cYmfd2PWEOUbSDd5_SazhoyrJRUYs/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5403572765493724082" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguilxWze4xvvxnqvtcADdH1bppJhN7fI2UIixb2QW8HkGX-tW6dTXsAoY8j2PPU0-IB-kcxOMNqvbx-qoXnRxjtS1ch4IlQ2QRwt3sMsRn2JsiPP4-JiTtcVcTv4NNZxHA3GVOVSd91rL2/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5403573761990431058" border="0" /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2c_4iqx88b7uNCmDCnIKnE-LL5pA525sCLxvdeHwwTTkMDL-1ve94SfgWWQapVZNKjM91PE6iwUzZBUG4JNJyxpJ6fqymOtlNUzT4ONZthIkhQVQd4Sm2IHorccuv5g0SjspwbLDpJRbg/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5403573760706433458" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpzIje7WYKpad8Z3jxGReQpt8FTzVU6s-xUER92aR5ZSeHGDpRV4l2kPHvH-md4XflzK1e4oRx_Nk9ukoTGnswmMyN712tR9QZjm1i2H7qvooLOKtgbZ7JS_dIz_YCVJ1uf5tEPodNAd3R/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5403573755326762642" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_iLHu-vk-4rP_Y7CZ_wN0ETh5jgJJrhZdGpvf_xY9ozAg3ZteNPuz804vvwCxaaW3mf972XgVmiEEalBoYP2fAAqqx8Q__8INHmjXNhBCFwINAfEEemKreDKnkFZgLq_K0YfUa1r96Yw3/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5403574403416761234" border="0" /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpzIje7WYKpad8Z3jxGReQpt8FTzVU6s-xUER92aR5ZSeHGDpRV4l2kPHvH-md4XflzK1e4oRx_Nk9ukoTGnswmMyN712tR9QZjm1i2H7qvooLOKtgbZ7JS_dIz_YCVJ1uf5tEPodNAd3R/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5403573755326762642" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVd47E9ZKoH_0ui7OBN9ukrFDLlv95IMRKUFHepz5nTb-8v5DFCZXdNgry-OT9xiNZL9v9urXYVg7xoJjOuSPEIuvXesUOqcDYkZvk_yKy3wpUkJ8mzdVAQGpoc5nYnrJneLtebRDVZ-BC/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5403574399056147970" border="0" /><br /><br /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC91SDAxfw8rE57oCxHzcXAXaXMawAFE8_BeYE_ZEuS7C8lc1Xc9b4wj3cMuhvnQkXy-FKpxf3ZRqWTivBqnHTvWxFHGbHr94Vb5IA3tTFUWM7fftjafxZ3ZdlGmDeSgcdbce7ACNZsCfp/s800/1.gif" alt="" id="BLOGGER_PHOTO_ID_5403575370716136882" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgi6XDOeDWl-XfHDSXDr5WrDJR_LUyvHe1rJAJ0DAX44GdzsxpdeHwo-nh9NCYWhUZKGLYi3yCqsqqSDq8mVrdFRxHx7CE74Dtf55qIpbQN3ZFmFqOMMKOr5wPSaUZ49_EtqzwjpsUoMvKA/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5403575367156195106" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDXvVmatMumsVDUzelCvt0-08m2RQHOkidvnyQqntDOF670MHe2Ff_R3j26YalekM2NOI4ANAb_KMV0PFwQ5Fju-6hEnjNaj0OYkmiZQp_0FwJA1-klrWS0tkrg-JaIG_KhKpykCtgT_Xs/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5403575361183947186" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnJWR_9Qmx5chJg-zLqlWN9kcaDBSYwGe8aGvMKjvqO3tdOs1OMeqoYzwOEVWmNSMJb91XjiVGSdHAb2ZPGw5RVvCGxG-OOWI9fRQS2zEHpc_iBVK4tjNyaFa5HE3fd8WAyfD6NIu_NTUj/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5403577002402491490" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________</span><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiBYUkQxbZyJGxnxLdF6TSfhP0aERLs9UrqahaeFlG8DLdGeYtjCVPfWIexvEA-MmuoHmRWz880tpn7Y0ubu3pBPndTaYUY9xBv6Ga3YbG7n8qChbOhzGamJV-VrkdIJgLXzR-Zp_fDD7C/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5403576997118418914" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________</span><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOX9vDlQ5bpV8Ant0fD6m2pptm-mpQ8q52WJu1C5aZyHnLkdiNRrIcR48lxDhIs4ZboaBYh5UyyuMNrdtDG-j70Q6fqqKA0aeXNYeyZPiP5xy0wdOM-hEAKbB_Ik5UpjAVx6KySOwRugtQ/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5403576993628129762" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________</span><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOSlkOdw1fIxZoaECJg5Zc-JW-2wP3h0Cnt9AJCe0SPSgK3quVfItnMkEZPnQoUbpqh00GQCJ-AH_UKjh70-X7lr3P8PRoQVHku_HrEOGKzFEpbLhLQNlJBKopB-1t-rqqB3NbqCALBIac/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5403576989104283202" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvebllbPuYMOnRJuc1BGt58GZWuY6rKe5UxeaQPi4tw5uOCwpd5gtDz66_2-16kF_dvbY0jpNwVJTfkZ8j476Zrvbnf5Zw8frwA-xU3-qU7mVtINaf62DGpxmQGL9w9Qy48308_0wOKKkg/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5403578270333042466" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIshx2tC-Udss9GcFQikpcrSpbJit133qNcK0zQDc838JKRf_k099gCvBscZ-S9F9Ia0qKN20A7kxUIXUGcMEhXBRii0Vn6kmoO8zvH_P_kK5ImuJqhVmba27ZT-kCpUjcCTKcAJOqs9DU/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5403578263756461170" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZeYo9W0HL1atne7s-ip-KMlL_TA8ZTtr8TOuVmh_Asar1iodf5mpTDA1RIwCS0cl-PqLga-NjaHplXqDh1UKvzvDaUMM2mEpaQm3OcfyQuWgr8GaHJ4pLa9mCupA8tMrQTiqfr5JjEZ6-/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5403578260721273858" border="0" /><br /></div></span><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);"> Soal diberikan oleh Simon Lim melalui email. Thx to Simon. :). Penyelesaiannya sudah dibuat:)<br /></div>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com13tag:blogger.com,1999:blog-8125318493233557109.post-36530013120055173962009-10-31T18:38:00.011+07:002009-11-07T07:46:40.168+07:00Rubik Cube<div style="border-style: outset; border-color: rgb(255, 18, 0) rgb(220, 230, 0) rgb(0, 72, 255) rgb(30, 255, 0); border-width: 5px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Rubik Cube adalah Puzzle yang diciptakan tahun 1974 oleh Professor Arsitektur, Erno Rubik. Untuk lebih jelas mengenai sejarah Rubik Cube, silakan lihat <a href="http://en.wikipedia.org/wiki/Rubik%27s_Cube">wikipedia</a>.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7l-OBSjZXyifuUmxAM5k6-Dipah7JS5RdOEGOkJ4s7PryFa6oHlqAel_elL6dyFwvRoyg3OOuAEfoKor6GfiFH_5jxNGmkAVOjUE-Wk8VQNL_3qVIriYgIuHq7aaLS6a60XkurNrZXprO/s1600-h/rubik_s_cube.png"><img style="cursor: pointer; width: 169px; height: 175px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7l-OBSjZXyifuUmxAM5k6-Dipah7JS5RdOEGOkJ4s7PryFa6oHlqAel_elL6dyFwvRoyg3OOuAEfoKor6GfiFH_5jxNGmkAVOjUE-Wk8VQNL_3qVIriYgIuHq7aaLS6a60XkurNrZXprO/s400/rubik_s_cube.png" alt="" id="BLOGGER_PHOTO_ID_5398730237313347586" border="0" /></a><br /></div>Berkat adanya acara The Master saat Deddy Corbuzier "mengalahkan" Abel Brata dalam "blindfolded" Rubik Cube, di Indonesia permainan ini menjadi popular berkali-kali lipat. Toko-toko mainan, aksesories, games, souvenir, etc semuanya menjual Rubik Cube..!!<br /><br />Ada beberapa pertanyaan matematis yang berhubungan dengan Rubik Cube:<br />1. Ada berapa banyak permutasi yang mungkin dalam membentuk suatu rubik cube 3x3x3?<br />2. Suatu Rubik Cube yang diacak secara random dapat dipecahkan dalam x langkah atau kurang. Tentukan nilai x yang minimum.<br />3. Bagaimana algoritma terbaik untuk memecahkan Rubik Cube?</div><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><span style="font-weight: bold; color: rgb(255, 0, 0);">Berapa Banyak Permutasi Yang Mungkin?</span><br /></div><div style="text-align: justify;">Rubik Cube original (3x3x3) mempunyai 8 corner dan 12 edge. Untuk setiap corner, terdapat 8! cara untuk menyusun semua corner di tempat yang berbeda-beda. Secara orientasi, tiap pojok ini mempunyai 3 wajah/orientasi. Namun, dari 8 corner ini, corner yang satu harus bergantung dari ke-7 corner yang lainnya. Artinya, kemungkinan orientasi corner ada sebanyak 3<sup>7</sup> (2187) kemungkinan. Untuk edge, terdapat 12!/2 kemungkinan untuk menempatkan ke petak yang berbeda, mengingat permutasi ganjil pada corner juga mengimplikasikan permutasi ganjil pada edge. Tiap edge memiliki 2 wajah/ orientasi. Dari 12 edge yang ada, 11 adalah independent, sedangkan edge yang satu lagi pasti terikat dengan edge lainnya, maka terdapat 2<sup>11</sup> (2048) kemungkinan untuk menyusun orinetasi edge. Bagian tengah dari Rubik tidak pernah berubah, maka kemungkinannya adalah 1.<br /><br />Mengalikan semuanya, maka hasilnya:<br /></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkp1CKAcJRlDw4XLU3PB11XPul9Dbf_BG9TTuuKcA7eLbX0NxIyQ7hZDY4dTIr-6hzDvdLHjwfgjs0gc3dPP_moO8-9RiPuTc6F26XVjlf6I9NZYXafFN7fnZWpaSDiGk0Qg1lIyjUn5Ou/s1600-h/rubik+permutation.png"><img style="cursor: pointer; width: 275px; height: 19px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkp1CKAcJRlDw4XLU3PB11XPul9Dbf_BG9TTuuKcA7eLbX0NxIyQ7hZDY4dTIr-6hzDvdLHjwfgjs0gc3dPP_moO8-9RiPuTc6F26XVjlf6I9NZYXafFN7fnZWpaSDiGk0Qg1lIyjUn5Ou/s400/rubik+permutation.png" alt="" id="BLOGGER_PHOTO_ID_5398743508740378770" border="0" /></a><br /></div><div style="text-align: justify;">Jadi, total permutasi yang mungkin dalam membentuk Rubik Cube adalah<br /></div><div style="font-weight: bold; text-align: center;">43.252.003.274.489.856.000<br /></div><div style="text-align: justify;">Sangat banyak sekali....<br /><br />=======================================================================<br /></div><div style="text-align: center;"><span style="font-weight: bold; color: rgb(0, 153, 0);">Optimal Solusi untuk Rubik Cube??</span><br /></div><div style="text-align: justify;"><br />Perhatikan bahwa untuk memecahkan suatu Rubik Cube secara optimal, dibutuhkan kemampuan analisis terhadap pola-pola Rubik Cube. Mengingat jumlah permutasi Rubik secara total berjumlah 43 Quantillion, maka mustahil bagi manusia untuk dapat memecahkan Rubik Cube dalam langkah seminimum mungkin. (mungkin bukan mustahil, tapi tentunya akan sangat sangat sangat sangat lama).<br /><br />Agustus 2007, Daniel Kunkle menggunakan super komputer untuk memecahkan Rubik Cube untuk menunjukkan bahwa semua pola Rubik dapat dipecahkan tidak lebih dari 26 langkah. Tahun 2008, Tomas Rokichi mempunyai bukti komputasional bahwa semua Rubik dapat dipecahkan dalam 25 langkah atau kurang. Selanjutnya, jumlah ini akan berkurang menjadi 23. Agustus 2008, Rokichi membuktikan bahwa langkah maksimum untuk Rubik Cube adalah <span style="font-weight: bold;">22 langkah</span>. God Algorithm (Algoritma yang bertujuan meyelesaikan Rubik dalam langkah seminimum mungkin) untuk menyelesaikan Rubik Cuba ada banyak, misalnya: Thistlethwaite's Algorithm, Kociemba's Algorithm, Korf's Algorithm, etc. Semua dapat dilihat di <a href="http://en.wikipedia.org/wiki/Optimal_solutions_for_Rubik%27s_Cube">wikipedia</a>. Ketiga algoritma tersebut digunakan pada komputer.<br /><br />Untuk melakukan langkah seminimum mungkin memang mustahil jika dilakukan oleh manusia, namun tidak mustahil untuk dapat dipecahkan dengan cepat oleh manusia. Ada yang melakukannya kurang dari 1 menit, kurang dari 30 detik, etc.<br /><br />Metode yang sederhana dalam memecahkan Rubik Cube dengan cepat, antara lain:<br /><span style="color: rgb(51, 51, 255); font-weight: bold;">1. Fridrich Method (Layer by Layer Method) </span><span style="color: rgb(51, 51, 255);">ditemukan oleh </span><a style="color: rgb(51, 51, 255);" href="http://en.wikipedia.org/wiki/Jessica_Fridrich">Jessica Fridrich</a><br />Metode ini dimulai dengan membentuk tanda cross pada layer pertama, dilanjutkan dengan memecahkan layer pertama, layer kedua, hingga layer ketiga. Metode ini adalah metode yang sering digunakan oleh orang, mudah dimengerti, namun membutuhkan banyak sekali langkah (boros).<br /><br />Untuk mempelajari metode ini, bisa cari di <a href="http://en.wikibooks.org/wiki/How_to_solve_the_Rubik%27s_Cube">wikibook</a>, atau di <a href="http://www.youtube.com/watch?v=IW_BBp3FPMQ&feature=channel">youtube</a>..<br />Layer by layer Mthod selanjutnya dikembangkan menjadi F2L alternatif, ZB Method, ZZ Method, dan VH Method. Lihat di <a href="http://en.wikibooks.org/wiki/How_to_solve_the_Rubik%27s_Cube">wikibook</a>.<br /><br /><span style="color: rgb(51, 51, 255); font-weight: bold;">2. Petrus System (Block Methods)</span><br />Metode ini dimulai dengan membentuk 2x2x3 block di cube, dilanjutkan dengan memecahkan 3x3x2 block, tapi juga mengubah edge di layer terakhir. Kemudian, layer terakhir dikerjakan dalam 2 tahap, pertama pojok, kedua adalah edge. Metode ini sering digunakan dalam contest langkah seminimum mungkin.<br /><br />Metode Petrus memiliki kemiripan dengan metode Heiss, dan Gilles Roux Method. Lihat di <a href="http://en.wikibooks.org/wiki/How_to_solve_the_Rubik%27s_Cube">wikibook</a>.<br /><br /><span style="color: rgb(51, 51, 255); font-weight: bold;">3. Waterman Method (Corner First Method)</span><br />Untuk mempelajari metode ini, dibutuhkan 90 algoritma dasar (yang sudah cukup banyak dan menyulitkan untuk dipelajari..). Pecahkan face di L, pojok di R, dan selesaikan edge. Metode ini adalah metode menyelesaikan Rubik Cube yang sangat sangat cepat.<br /><br />Metode yang mirip adalah Jelinek Method, yaitu metode untuk 4x4x4 cube. Lihat di <a href="http://en.wikibooks.org/wiki/How_to_solve_the_Rubik%27s_Cube">wikibook</a>.<br /><br />Untuk mempelajari Waterman Method memang dibutuhkan kesabaran, karena lebih rumit daripada Fridrich Method, namun sudah terbukti keampuhannya dari pemenang Rubik Cube: Josef Jelinek!! Silakan lihat sendiri di <a href="http://www.rubikscube.info/waterman/">situsnya</a>:<br /></div><div style="color: rgb(255, 102, 0); font-weight: bold; text-align: center;"><a href="http://www.rubikscube.info/waterman/stage1.php"><span style="color: rgb(255, 102, 0);">WATERMAN METHOD</span><br /></a></div><div style="text-align: justify;"><br />Untuk menyelesaikan Rubik Cube, kalian bisa menggunakan software yang bisa didownload gratis di internet. Semua rubik dapat dikerjakan dalam 20 langkah (rata-rata)..<br /><br />Note: Lihat juga di situs resmi Rubik di <a href="http://rubiks.com/">http://rubiks.com</a>.<br />Solusi Rubiks.com layer by layer: <a href="http://www.youcandothecube.com/secret-unlocked/solution-stage-one.aspx">http://www.youcandothecube.com/secret-unlocked/solution-stage-one.aspx</a>.<br />Saran saya, pelajarai semua metodenya. Layer by layer, block by block, waterman, dan berbagai versi berbeda lainnya. Menggabungkan beberapa metode tersebut membuat rubiks dapat dikerjakan dengan lebih cepat :).</div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com2tag:blogger.com,1999:blog-8125318493233557109.post-19773043496749362042009-10-20T07:16:00.063+07:002009-10-22T19:36:59.178+07:00Chinese Remainder Theorem Eksplisit<div style="text-align: justify;">Di post sebelumnya sudah dibahas mengenai Chinese Remainder Theorem, tapi hanya dijelaskan solusi yang dilakukan secara iteratif. (Lihat di <a href="http://hendrydext.blogspot.com/2009/05/chinese-remainder-theorem_08.html">SINI</a>) . Di post ini, akan ditunjukkan Rumus/ Teorema Chinese Remainder Theorem yang eksplisit yang dapat secara langsung digunakan untuk mencari solusi.<br /></div><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzzF0M4Deuw59iNVtCXanb4MyglTvynQgZ7qNqv6DQB9HA1att6yibrswDSoxBDEcCHOAXWlf5djoUE6yIBXKungTIxEWeiz9xvVmz6JMysOJvu6XX1JR6-Nl96BqhDusybtcvOF2vt05L/s1600-h/judul+copy.jpg"><img style="cursor: pointer; width: 400px; height: 34px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzzF0M4Deuw59iNVtCXanb4MyglTvynQgZ7qNqv6DQB9HA1att6yibrswDSoxBDEcCHOAXWlf5djoUE6yIBXKungTIxEWeiz9xvVmz6JMysOJvu6XX1JR6-Nl96BqhDusybtcvOF2vt05L/s400/judul+copy.jpg" alt="" id="BLOGGER_PHOTO_ID_5394476148193329650" border="0" /></a><br /></div>Diberikan sistem kongruensi sebagai berikut.<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5U3w_xczyTPXsD0xjBI2AllTbvFv3npCzjs-Qk1tfjAgxEGjNhOMk0KNDkho9r4HOofRcB8L9Rv9Su2ecF9aHYNCVjO88dlGjgxUlEyKWKn2spvSq-k3BKiSdXlehyphenhyphenAvbovEzkPDTl4Mc/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394474367449440466" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrfP9NNpoHliBInTb0knn2fF_LjSyyx2qRpGH03RXGvmXw44GGu7FgkCbW5VG9mD4YyIByl8cx_xkZsDPwgGgDLgbulPbDokAp6nPaTCs4c4kOHlefRVSIZm0Ze5Ff7sCTIFqhHiHDWXg/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394474359198437810" border="0" /><br /><span style="color: rgb(255, 255, 255);"></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvnIy2FusHaIk5UcQsZwL-ig8UBWaivpr3hkpx8_1tbRvoIO_5_cNrq1e7-SMD6JnGFOnt2k0XekRA8zc27cpzSRwi8nM1t-TjqQa3EdSR6tgJvXuSvVgeZuWjzO-yQM60JKQazUlP7Gmz/s1600-h/5.gif"><img style="cursor: pointer; width: 3px; height: 15px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvnIy2FusHaIk5UcQsZwL-ig8UBWaivpr3hkpx8_1tbRvoIO_5_cNrq1e7-SMD6JnGFOnt2k0XekRA8zc27cpzSRwi8nM1t-TjqQa3EdSR6tgJvXuSvVgeZuWjzO-yQM60JKQazUlP7Gmz/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394476659723703730" border="0" /></a><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPp2yZZhN93w9zTOWcOFsfrbkpWVbwcnnE6-62eEBhXKyw3cz7puztRJhhwM-czNMoLGVxPHkW7nXC-axCARkLpDNBFWfdrUqR3nzCBpheBNWLSXKfEbGjmJvkClT6a0x1J14RpHwSBkw/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394474341133413362" border="0" /><br /></div><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjwgkasRn7cMDY02o-UNGhKk0oqH-QljQu6O2LCoOuM5DGM6FYuJfD0liCjqj4L2cNrtC_HZvVWkSJ47ABwM8l1_qM5VCDauYxgN1FzRwS6aqVSbaaPJB3xNdY-2ItBSvURK7uA7Z4lnmh/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394477387211718578" border="0" /> haruslah saling relatif prima<br />Dengan demikian, kita dapat mencari nilai <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV4o9BTv5q0QyiGGg4nl8gdxRCsWPKOIA47YXJpN1QAU2kGtLAmULMhOe6zXlgCMyfotEURh1aHH4zVwhth1IZv9xV4Z-NiopqIQJ3i3kT-el_w11VbbE4fddS1szpf2EAzJpjcFXzM1zJ/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394561380916304530" border="0" /> dengan rumus berikut.<br /><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7Z00WR1pUUhI7jLs4h95wyY1_huabBMML2XsNsZxWwFmPhngSleN0IxWTTT9-brvv73ACXGXL2GCSMk6qXVL1d1tjy6F8cJ3fY6dCcNbX1OOhtCmVQPDf2hmpKRy9PDckKry7qfnDuTDg/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394561371067336194" border="0" /><br /></div>dimana<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsqxGN9wU4eraa3aStljymCGo-2gnpPkpyEGsnUbVFjpmz4OLRcGvW53mKS8SpaaPjdfr8Q12UXYEnFOtQGUpKd1pd4sHlBJLTmgHY-yD54I86lNjiqudIJXWgtHGEmHl3SIqYk1bFA_dh/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394562756661565074" border="0" /><br /><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSYCBVTf_GN0_-bLEnjy37xhY7hUXazxhN_Z_I5SE0g6tU1zQJTY-U8v7SSLM98DEwSWv4LelbJPfiqW3TkGAi5fxts-LWxR8MFfQsaYvPwblmmCcH5lHABtkWE3k2t_AVbyj84A1aEKyc/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394562738162099058" border="0" /> untuk setiap <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAqauOtt24nyjWAm8DQBhngZXWyRKd_JWnH2m89HEUmyvtPBpX-jxKzy1ufRvgGe-BqKdWft3JPzBHurpR3yA_m2ey1C0xaqZB4p5gt6YkamSrWjjXws_Y8I-gnVk2jvb0yrW2P2ik8EeC/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394562729765995410" border="0" />.<br />dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1g9110FbIv0zgm2AOq82az-bB_6-TPVPl9vEfJoVm-nR7iGdtGVpQKj3Rz9ffw1qRKvAI17aiODdlNUaXTs6uOA0VcMQxZ0H4v28lBAaOwFfCNN4Sz7wj6jGWM0gJ5IHOlB4FjULPjqBB/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394562721103809458" border="0" /> adalah invers dari <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPZFFh651YfK0xlst5Rdp2hyphenhyphen6t-9nJVBeoCR0OdDD2hUvm_pk_OXQmX6hnQvwyhJRoFPGYeRNdiLDvelcwSjD9xcu1S1bV8aOIjyE7FkIrRGbTTLrTHNFMh5mVcdOFD7hYSgTpE0NVuu56/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5394563634318503922" border="0" /> modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiekxsOsvdcPfc8biQd6lalbg62hQJa5A834GUMupQkk3bMjAvoJfdqI8M4KgqZy2jnBLCfjv90XK_zuZJVBae1e9QQ3TdoFKaJNJTfDpvyz1hWbFfR7O47IMP1x_d3VR8qqi3oMw3vblcg/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5394563626689656946" border="0" /> untuk setiap <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAqauOtt24nyjWAm8DQBhngZXWyRKd_JWnH2m89HEUmyvtPBpX-jxKzy1ufRvgGe-BqKdWft3JPzBHurpR3yA_m2ey1C0xaqZB4p5gt6YkamSrWjjXws_Y8I-gnVk2jvb0yrW2P2ik8EeC/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394562729765995410" border="0" />.<br /></div>Untuk lebih memahami, silakan lihat contoh di bawah. :)<span class="fullpost"><br /><br /><span style="background: rgb(235, 78, 7) none repeat scroll 0% 0%; color: rgb(255, 204, 102); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-weight: bold;">CONTOH 1:</span><br />Suatu bilangan bulat positif akan bersisa 1 jika dibagi 3, bersisa 2 jika dibagi 5, dan bersisa 3 jika dibagi 7. Tentukan bilangan bulat terkecil yang memenuhi kondisi tersebut.<br /><br /><span style="background: rgb(235, 78, 7) none repeat scroll 0% 0%; color: rgb(255, 204, 102); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-weight: bold;">Jawab</span><br />Soal di atas dapat ditulis ulang menjadi:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhj380ggLDcjGE1pekecLwmMF72B8SYvEH9gf-mMOGUOrcnNw-kJvbpwW19VPKjKcome734q7Z5LXiVAtJ8EF4qaNDB4unlv2wQ1OadT7ZLlvrtJ7HStUb0jjIi7zvaRDEnuNpLJMJQxp6L/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394566138572560818" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifx9IbEWwJl8fXdOK_G92F_93szFpq2Q8HtQR9CLG4LlvWPM3s_4-F17vadaqWDO0vQaKRaiNV68DMDhCT4zkdVKDwmsBlTemsSSsb75FPNxtOdpHWVh5iWTzhFwuJUms2CdG54J5vBgxC/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394566129456064082" border="0" /><br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2a2aadnYn4ZW1wXIyMKIPgI9IuJAOchwTxWYq4rttlO4QIZ7TOA6lp29fyid0IOY6tdhJhGGYqfc8NK1Yvo2s-1YsXnawHQuEcK7M02oNPZqBezDZgu12QZmX_sbNKWo6Zf8Iz4CWMwq7/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394566122730459714" border="0" /><br /></div></div><div style="text-align: justify;">Karena 3,5, dan 7 relatif prima, maka rumus CRT (Chinese Remainder Theorem) dapat langsung digunakan.<br />Kita dapatkan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz-Erfz1AHvb-U9vCYYDoQMtYxhYfmG9g1A76FmqzIG12i0-FkoF9JEiG5EvoshzsJSx9PZ0dBjw60IXvguFlkqrnUflzG8RPRVbaydR1DX1U67Q5i6yjHH-RIRxn0qfRW-jXUISz8galW/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394567672149973842" border="0" />, <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhklvWeLxak0Cr3gH9Wu42jXctjNbAYJCDCCfaG7GAbmLzpbPd0DTdq8Mv9DXSm-GZT4BtXjufsYRcidAg8j3XY-VbYMJS6cZDdPTbnIC60K0sE9wclJFKjRBJRynk1aVCiDVUD5CdbYB-8/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394567665674532818" border="0" />, <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk0q-XVTaEl_HAuscYA7NxykWsKV0az_GY5F8SjO9RYCeei26wEUalQioYTvpCmkbHBf7ynV7Bf0Hp7aGhq0uv8jrLynUb1e9l1yboY091GZujhDtN9f4jb67moZB1lARInOXNi0JaxzAL/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394567656452323922" border="0" />, dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0xPMadDhodPh1WL5awJeZanLOLZAYTCFg1qdkUaM2wdmiCa3Hxy0di0fmNehDBf3gNEw-RG1DV7v4FeEVICwfmoVTnjqb5jHVQh0RypAn1EDOfd8N38JmLH0ZsDATBWxYzCh7VyNoPKNR/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394567642466539938" border="0" />. Untuk menentukan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz298rPsBEZcbZgljBp2n3WCTglrR1tDX13Ow6GzaEJ_4I7J6Wvq0C8siAtV5h6qnd37767tp6FSN21pPorznNMzOOTSVh2iz4r3V-TN0zk6JzVWeX29pxVW1qnofP-sGLwAJHMKDNrizI/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394569807999622402" border="0" />, kita selesaikan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-UII54phDXvJ8cR1yKHOyGmJmH5RDDPzpUWVZxu2l5eevLcHd-IGhqlovqknlS1t4gh9DWWOSyX-3uzX3Q8NQZXwmDbXBTkps6-AIszHbMVo1cBr33ZERo_0xMC_qm9E8OtMJmK34hqpo/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394569798448387666" border="0" />, menjadi <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirEReb7N82RzfHhZJql-_JkyMC3nGWrMZGorbLyZxee6XXrIt1ngny9JGCXMJehFrVOJnZGZW67rFny4T9-PBdJCY2ErbkU5rr9Yd4-_MrsyfO4NpRMjkKEDwwEoi3k1-dSaKQIR0MVK2Y/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394569779926434354" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxMOvDu_6jSwIUu_dXtz1SgI83k9VhiplhKX1zLcRqpsCZGYCdO7AlPmomindNqB8SIhjnNaiYhzKXv27hpwayZejLUMnSzAFbtFMWQXx4E-6JxkFledg7TH8SDfn_vE9JMnGuc6x3ShFu/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394569762132516370" border="0" />. Untuk menentukan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKkXYcPzxdnZPJ-Vsc4WeGEwuvGQGlGZW4p6P41ARDraqrB-MZXL_pm3Vmp45hQKCzZzPvzYmUKBkuMqYkbuJYFsj4yA8H557cseISf5FLSpFx6NwBYtfH9jPQScVjhl7D0055qmtyxgdR/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394569737553008770" border="0" />, kita selesaikan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgi-cfs_KHFD3jtjjEdzm1Ck_1VHdAwzTm5OuzVMbbMzCrisfp4_Xz6NvDMjgmoy2Has-FgI7o7HT9aYWm04AWVfI4WSjdvZAKUJXwn97yYO9Cny0ao76W8JQyt6yb6BkRw1s-dGHqCUH3N/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394569531100371954" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjh_LdMk3BQNGv_2OyfiYUtvw0UHcI28sllHHFPIc34IZ4Re1T5o3aaSWCA9uGapawYkKl4vvXJx5p5nEXmdSnAZkx0gxmhtgOGzvu4ezMdrJnekremufv8UuHfX4jpoB-g1RDmkI-CfUrJ/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5394569522410444338" border="0" />. Untuk menentukan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI8Zr2sVVbGtvkVMJdnhMPsgqDVIjvJivf0pRl48p_GjxBb43sYzr2yDUHoKFQoZRK0vflGCbO7JywgZA8ZXsCR3NQg7MwoA0E2F7t4pgIoaEjY4rDHn6T1n-pE4onejiPybRLmRGwFzbk/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5394569492531746722" border="0" />, kita selesaikan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEholppltmLGPkq0t5mj2yNzp-TEibbcRH7aPffZlm39EvuCNQZTEmR9ogIiyhj89PddSnOsoHWqqxllW-MzaQAKk1fjLwnFhPwZN55uUjjHnJpJK79LbVw-S2CvFpjZhGPNBzI-XVotBf9C/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5394569516238952450" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKSL89Px9R8WpKRpnjoQFsP88PCuUhX1cvamCj6gfqX8SjVHhfxg3sv4_xsQJTBSbgGJ2Yk6TyGqWsT6MWyTiDsdKbuYqT8BnddYH7cy3SbihnLzA0_OX69lBK-03k80hG716GQbowup9o/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5394569501823113970" border="0" /><br /><br />Tinggal memasukkan semua elemen yang ada ke dalam rumus.<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNbpH7GbJdTybwwYw4mbXSwjgfaGngpasqaOdt4QSZe6Ty1d6o0N5rnlpY_H1i77CcPRONtMS_BZPWsZj8rvz8_0kkRGdcUq2O1LAPlFYImdSo6YRkPsEppx84UvtFK1V4qBiexPYkZjBx/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394611889953119234" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuA8WV_pbCQGtB2umvTG-RPt-8uVZc0iGgOurYuxA7TWMxiSb8NmPWMR4YzzVFQ55V67ApIX-aohrJmd9KWfzx9rFWiX1i6z5uUp2Bye-gYsfvVKyknfa70rW6RO5RAgK8xUoIcFL9jF32/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394611887054789186" border="0" /><br /></div>Jadi, bilangan bulat positif terkecil itu adalah <span style="font-weight: bold;">52</span>. Bisa dicek bahwa 52 akan bersisa 1 jika dibagi3, bersisa 2 jika dibagi 5 dan bersisa 3 jika dibagi 7.<br /></div><br />Untuk membuktikan formula ini sangat sederhana. Lihat kotak dibawah.<br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQnizt_bzBt1ZqWR7MWvO9VBgpMDrU9_WlYHBULpx4IeO738m5hTHQXt364Ejq6J89jHPRLjePXDSWsc1PUVcsK2CrA2HwKWGa3WckEhe2Bshx9-hVc6lLL5tUXt9lPAp4nkFJXQf7GoGZ/s1600-h/judul2.jpg"><img style="cursor: pointer; width: 400px; height: 29px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQnizt_bzBt1ZqWR7MWvO9VBgpMDrU9_WlYHBULpx4IeO738m5hTHQXt364Ejq6J89jHPRLjePXDSWsc1PUVcsK2CrA2HwKWGa3WckEhe2Bshx9-hVc6lLL5tUXt9lPAp4nkFJXQf7GoGZ/s400/judul2.jpg" alt="" id="BLOGGER_PHOTO_ID_5394613936039393154" border="0" /></a><br /></div><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5U3w_xczyTPXsD0xjBI2AllTbvFv3npCzjs-Qk1tfjAgxEGjNhOMk0KNDkho9r4HOofRcB8L9Rv9Su2ecF9aHYNCVjO88dlGjgxUlEyKWKn2spvSq-k3BKiSdXlehyphenhyphenAvbovEzkPDTl4Mc/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394474367449440466" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrfP9NNpoHliBInTb0knn2fF_LjSyyx2qRpGH03RXGvmXw44GGu7FgkCbW5VG9mD4YyIByl8cx_xkZsDPwgGgDLgbulPbDokAp6nPaTCs4c4kOHlefRVSIZm0Ze5Ff7sCTIFqhHiHDWXg/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394474359198437810" border="0" /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvnIy2FusHaIk5UcQsZwL-ig8UBWaivpr3hkpx8_1tbRvoIO_5_cNrq1e7-SMD6JnGFOnt2k0XekRA8zc27cpzSRwi8nM1t-TjqQa3EdSR6tgJvXuSvVgeZuWjzO-yQM60JKQazUlP7Gmz/s1600-h/5.gif"><img style="cursor: pointer; width: 3px; height: 15px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvnIy2FusHaIk5UcQsZwL-ig8UBWaivpr3hkpx8_1tbRvoIO_5_cNrq1e7-SMD6JnGFOnt2k0XekRA8zc27cpzSRwi8nM1t-TjqQa3EdSR6tgJvXuSvVgeZuWjzO-yQM60JKQazUlP7Gmz/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394476659723703730" border="0" /></a><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgPp2yZZhN93w9zTOWcOFsfrbkpWVbwcnnE6-62eEBhXKyw3cz7puztRJhhwM-czNMoLGVxPHkW7nXC-axCARkLpDNBFWfdrUqR3nzCBpheBNWLSXKfEbGjmJvkClT6a0x1J14RpHwSBkw/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394474341133413362" border="0" /><br />Tentukan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxpWyfmfVNYWZztJJrhVqsFT-UuxN0kBgKuNCDmhg-dFQTgaxigUlJorrqi6h3lMgr34kD8krnYYgKER6p98WfJvTRToMST-C2Eu4jBMx505D4oB55ZZvS14OkRa55fqTc__AvNHqP3bwm/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394645268628091554" border="0" /></div><br />Solusi yang diberikan adalah <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7Z00WR1pUUhI7jLs4h95wyY1_huabBMML2XsNsZxWwFmPhngSleN0IxWTTT9-brvv73ACXGXL2GCSMk6qXVL1d1tjy6F8cJ3fY6dCcNbX1OOhtCmVQPDf2hmpKRy9PDckKry7qfnDuTDg/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394561371067336194" border="0" /><br /><br />Mula-mula pandang bahwa<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn6qmCyI8B0f4zwL0ofJCtvC5e3x9LHe1AY17oz9edGeL2pY_m82_pjCwhZ253g96GW3m3LuU_DCVochJWBOAus1tOQ43VF0C721T-g1JKpCJoM0BOlEEsqLS61tW3RgiH-Z4TSpo3XoPT/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394641945934300178" border="0" /><br />(merupakan solusi yang sudah didefinisikan sebelumnya)<br /><div style="text-align: justify;">Jika solusi tersebut memenuhi syarat awal bahwa akan bersisa <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirzhPISY9m550o6YH0Ktd0UTPJVBQ-qoiMrq7zNCgMhhkM9gN8icE5DefwaEbzU5r4hLEKx_NESuUOBBazOuZZfNq-Rw4tcU1kLRQ7pCTkwwlKAiPMnp8IHqCeIHmpaGUCV5uvX4E37ILg/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5394650599207585858" border="0" /> jika dibagi <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4kEUEt7zWUm-2Masy5fYfG8Rqh-Gx_Ie3lBif1ga0n62ckqzEncTfJHdHo92s6Z2RdWLVLLkPp-LXX6nVEW_fgTy4GcS982AcidlsTBNaVWasw2d4V4Il_VMu_CYcHID4b1cRIXHzilLy/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5394650591945507346" border="0" /> untuk setiap <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAqauOtt24nyjWAm8DQBhngZXWyRKd_JWnH2m89HEUmyvtPBpX-jxKzy1ufRvgGe-BqKdWft3JPzBHurpR3yA_m2ey1C0xaqZB4p5gt6YkamSrWjjXws_Y8I-gnVk2jvb0yrW2P2ik8EeC/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394562729765995410" border="0" />, maka solusi tersebut terbukti kebenarannya.<br /></div></div><br />Kita coba periksa sisanya jika dibagi dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhog2ueANf0U39mPVpQA3E_hbM9HrN5eoyU3-AxOgWKCZYLC6e0vvJAH8vk6ZDGddZztiS6VIve8sN0vQk2gwiZLtYLP9rp4MNCRdQnFnaBf64jksOg2tu_0CHkml6GbqLoexraFgIsprJJ/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394645475212158514" border="0" /><br />Karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNB4GTUKPv-yApXqlCSK8pGAxW4tVT0io0sa0H3shck-8gdTZxpB0nNBLsMBUJ4RNxNHXl6S2BxHqyohzSQD3FLvtr3DPdWch7RMp_JhRUCcwWesXwbMCYysa8O3HEPvVIphOBATXJldAs/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394646928967441250" border="0" />, maka tentunya <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuckkAc4xujD8ldnRwVOX6Ic_6Hcg9HLhxhDZLMmXynGQV5Y1YJxe8LfBJpBHyy9kyvy7C7c4dE-ZzX4Q-f_FHd5lBRTa41HOF160DZpdJHiiaiOHmG56-EpsTUAXMyqYjTPmxP6qEwRXp/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394646685150044482" border="0" />.<br />Karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhreIqyZ_9Rsb21lftlFlG1z7KOwvKqabtF8o2fW01DncITRmEKkwMOeS_JNVSlv_TYytSALlSUaYI-Jo1_1kRMU0dqzGG9Rj1gbQG_lhYzVU6fXT3k1jq_LobathHyr7Gm1iJz1_ewXDCy/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394646673452462018" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmZ876mZHKt_IjdiQik7aYJ6ZFUx_rfwdJ_6BZ1c6PRa2JerG-KDllxk1amS-1c22jpjtS-eUzF2EJ1TFDSKb0qTvnyEfNJejeunmxqMLUNrAvrL9n6QfPNZYiUr5pygNmXHt4oZt4peiP/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5394647560381453762" border="0" /> juga.<br />Dan seterusnya dari <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg22XElQfsHZCMh6sEfUUVA0VeV9LrI8wRVVXhHEa7Nez160Jzx_tSnIr9gfds3RmqLAyJP7qNLzWVzmHSzIcNLZT5e1iFBVGXeK0MybopsJkTXFalODYdfYab8BCNCb3beNNfxctOss6Fw/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5394647549584276162" border="0" /> hingga <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwqEmYKfQ_c0zBIdaVbYlggCIyhKGO2oAZLEfWIoUuLcPiCr54vAa85BnulGlXet4oLJ17SWKthbFv-A3JBndX-LdHDnwMgeQ1UycrV0lbgH2xDogGOCTteEYO7NTNdEWg8pmN-0oZdzg5/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5394647545172171826" border="0" /><br />Oleh karenanya:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgywnpjtT_ENKMv0xO_tpdumrOe6esfFGuMMV8LiZ-d87wQWQlTfJKC5X8rtDmkCCfi3QERSuKae9f4GofmRLVjgwDpu15VDbK7f1C_oAYRV47CUhw2gl1-d-lnPemsh4Mdv9UwBLRiVGFk/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5394649052013179442" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFSpAtnMDI4N2N5d6ivxEi-ta0AeQSxbwSj22RwCjzfgiy9rqhlFmm3SaOJGlCKTrt5u1uu3izsuJzJOEe5WICuNdc-vvDPx3kIC_2otpBJu2nYv8fC9FLWWf83iF0qdnjoICjlIqCbIQe/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5394649045883944802" border="0" /><br /></div>Menurut definisi sebelumnya <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlvFyY304bkXtupRt1s3ZVhEeNHWV0RrUTd_qdVz3kTUIXbuZTtm7Nsxhgm8f6PaqG0OTyDpYnflTGRQVpj3TGPDQjYZLJZf7P_-239pXL-2jgaCmoVzAGSgHpW1VbwzZnfeQYogE1B_0O/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5394649550065222898" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5U3w_xczyTPXsD0xjBI2AllTbvFv3npCzjs-Qk1tfjAgxEGjNhOMk0KNDkho9r4HOofRcB8L9Rv9Su2ecF9aHYNCVjO88dlGjgxUlEyKWKn2spvSq-k3BKiSdXlehyphenhyphenAvbovEzkPDTl4Mc/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394474367449440466" border="0" /><br /></div>Ternyata, jika dibagi dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhog2ueANf0U39mPVpQA3E_hbM9HrN5eoyU3-AxOgWKCZYLC6e0vvJAH8vk6ZDGddZztiS6VIve8sN0vQk2gwiZLtYLP9rp4MNCRdQnFnaBf64jksOg2tu_0CHkml6GbqLoexraFgIsprJJ/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394645475212158514" border="0" /> akan bersisa <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlhT1HtgWB30THVNW_-3Dw2ZOG_kGBkzELoIeQcnLUUPFYJ6T9bkk3I1JOPM8IytHsbVjLHIhwcLFIjWhH_B8WsPdW6Qw90Xy8JgbSlRLdTvF1RewfRsmV1A88DD1Ku184MIMTv-cfamkA/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5394651474652998386" border="0" />. Artinya, ini sesuai dengan salah satu syarat yang diberikan.<br /><br />Pembuktian masih dilanjutkan dengan mengecek sisanya jika dibagi <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_HoUeo2mPLtxYzDIiQwjFo8qOSqVkKqXMoG_YmBSS_c8Ozct7rTCiEO5dQvO2nFhQGTMJWc3KE__XPVfBGcdNj42ONhzLJgGqXbaLLNqaOOVCuxrE9I-ll1BR-OnsIzg9pj9EalrzSaVQ/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394849675206097938" border="0" />.<br />Karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz0kr_5yD8xozHMfvMprccuZLR5XeinBkMCcHNh6EFIMBoQlwg9boO9znaj8WVljVvy76xLl01y-Jh6WMq-zIDD2QmGjQ4XusWVeDfmY1s43otP-1FlALMdZySheEpr71QLkh4PxszJiI6/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394850200646685090" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGbWNm7pigJIcf5zwuewQHcbf8WdbyH60j7EfBzBG9Rtgq6vc79TRT2o8MSXwC3CBtRHo_9ewknxaN6Yml427WciX8MjCztHTyh_9rQdhAOz5PSUpVZyVI4vJoKIukZfoOOHLg8kX_rP8F/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394849659982454626" border="0" /><br />Karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhreIqyZ_9Rsb21lftlFlG1z7KOwvKqabtF8o2fW01DncITRmEKkwMOeS_JNVSlv_TYytSALlSUaYI-Jo1_1kRMU0dqzGG9Rj1gbQG_lhYzVU6fXT3k1jq_LobathHyr7Gm1iJz1_ewXDCy/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394646673452462018" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCUICJekGHWuLUpbLIFvq41axxyqhHic_ZIrm8tE6wQ44zIELG1kQNzc7iKwkfwuHIuAKlc-PgtQxK092psdKlKDHp8YB0puLHex8n27SEXIAnjZcW4k1JsO8P4IEWU-tIr_rLAPFnfd65/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394849643205743106" border="0" />.<br />Dan hal sama juga berlaku pada <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg22XElQfsHZCMh6sEfUUVA0VeV9LrI8wRVVXhHEa7Nez160Jzx_tSnIr9gfds3RmqLAyJP7qNLzWVzmHSzIcNLZT5e1iFBVGXeK0MybopsJkTXFalODYdfYab8BCNCb3beNNfxctOss6Fw/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5394647549584276162" border="0" /> hingga <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwqEmYKfQ_c0zBIdaVbYlggCIyhKGO2oAZLEfWIoUuLcPiCr54vAa85BnulGlXet4oLJ17SWKthbFv-A3JBndX-LdHDnwMgeQ1UycrV0lbgH2xDogGOCTteEYO7NTNdEWg8pmN-0oZdzg5/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5394647545172171826" border="0" /> (silakan dicek sendiri, dan ketahuilah mengapa demikian)<br />Oleh karenanya:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtpXd5Tyj2hq4Kc0MR4pNzMiBni7m0qvlx0ocz-k1xJMo8U0MrbClUbcOHp2IeErCzVEu3RSoOCTW35_y2K7VR9AGIlrqE9-djpnlXnVoQLBSSurnmlTREm09JKkpfI5ff9nyM-h31GlCp/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394851098343771746" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEw_F0feduNttJ6HO4zoWa16eBJRIcexD0-hEV7NC8z4JZtkrXbZVifqIFjQP0KENVZqnzXg8VBiwW7AGb2u03jPM7wYS7CT1MVbYCc9AtUj595lHPIg-TVvocN9cU1_l6VHoejNHIQagd/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5394851030405730530" border="0" /><br /><div style="text-align: justify;">Karena kita tahu bahwa <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfQ3jgmRmoG5ULb5jLpbaygK8Azr3SR6264rvtq7b4yQztTq0xhBRkQedkoKtzyM-tSJplrWrp1B9Z3SirMy1F8Y2fN6x7pooOvzU766rJfCaMxFUbe02JoBhMW-3qCUBAprnfNYIjHH3Q/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5394851020545678722" border="0" />, maka<br /></div><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgu2cv0AVF38GDv7u6SpsNU3V_dVNdRxu4uXc5pP2_RgFOCLQgHzn2xZUiq9Az2BZGaMw78wawu4bkvTHEpsjE1U0WNIegp1XkVhU57AoklnHhaSN0vqAqGVbiOR7EZpVNsAwL1LwbkhhXa/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5394851018257685602" border="0" /><br /></div>Ternyata sesuai dengan syarat baris kedua.<br /><br />Pembuktian dilanjutkan dengan mengecek sisanya jika dibagi <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzhb4QeLMhVXDfbPg3aw__CTbAU5RUbK4LCsM-IOaFe6MZ0KQG_MzJEw_gmF5RPYmm-NoN-DnJmpNe1KvqzyhpxUXUJrxkq6KbyEbAxDJmxfpZoEeZl6eNZu3j72QJQFEjTYbzAPSSgNbY/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5394852084092688834" border="0" /> hingga <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhV-G6E2lz0LJynswbrVo_K0hUh0Gu4CxxhtwfBKZ1SAqZh869j67BkMyesuTuV056RISttvVHO8SgLqzVMPG5ofZSo_ZE7EAirisbKgV6ZpIl54uKbNAQ6ozMKd7nC2f37z92aDqemMW6/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5394852083369186402" border="0" />. Masing-masing akan menyisakan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhFPk_iIgQRAt-Fx2rwICi9hZ5ZS7Ju1TOyqO2b_9ffLPS4zNsfEwV5vHfDq5Fblng9JlF0SUxNhyGSjR7GYulyM-B9ZBRc7PG10hH_ZsEo1SH6Xqyvye3Qf2nrnhPtXekrDWJUc1q4PBa/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5394852774374748658" border="0" />, hingga <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz_eK5cBxCCJZvDA94fQbagLQtJFwzLLrqkiq5ChumutveGfreGgM9dYYEJzaj6VwoL_lYZ3sqVXGfGGOaZJkL6p1ptCp0QeC4Q51w9xdgrBHAE5x150Odl4_eka1MkSCmuglMhEvQ6dkp/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5394852767456055362" border="0" />. Dengan demikian, definisi awal yang diberikan terbukti.<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn6qmCyI8B0f4zwL0ofJCtvC5e3x9LHe1AY17oz9edGeL2pY_m82_pjCwhZ253g96GW3m3LuU_DCVochJWBOAus1tOQ43VF0C721T-g1JKpCJoM0BOlEEsqLS61tW3RgiH-Z4TSpo3XoPT/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394641945934300178" border="0" /><br />TERBUKTI sebagai solusi CRT<br /></div><br />Namun, ada hal yang masih perlu dibuktikan. Karena <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1g9110FbIv0zgm2AOq82az-bB_6-TPVPl9vEfJoVm-nR7iGdtGVpQKj3Rz9ffw1qRKvAI17aiODdlNUaXTs6uOA0VcMQxZ0H4v28lBAaOwFfCNN4Sz7wj6jGWM0gJ5IHOlB4FjULPjqBB/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394562721103809458" border="0" /> mempunyai banyak jawab, akibatnya <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxpWyfmfVNYWZztJJrhVqsFT-UuxN0kBgKuNCDmhg-dFQTgaxigUlJorrqi6h3lMgr34kD8krnYYgKER6p98WfJvTRToMST-C2Eu4jBMx505D4oB55ZZvS14OkRa55fqTc__AvNHqP3bwm/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394645268628091554" border="0" /> juga mempunyai banyak jawab.<br />Misalkan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1b5z3yqHf5J3cKJeCOyDO61Bxjo20gwiZRgU725QoZolpQlRQysTjpalytFvwYmHFMXkibj4Gy5za3u9K8gRcah1577l4XPruHDKDZrUrVi1A4nGtJcEyhM1mpzrdqpy2uyijdrpRDhzn/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394854345955974530" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVdvKPiOEWuHmw1w6ET1n3Yd_39Zy_zWRzaDhMp4NsXXSQCRbDKzsaRWiuWN2878J-bkJlDYMWZfPSOGqLdfrfp62s6kaORl5JMX_CxBL-FWM090aItfQUoJeWPPJs9vj_3QSaAjNrQ-Y8/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394854298374882786" border="0" /> adalah solusi CRT yang nilainya berbeda, maka:<br /><span style="color: rgb(255, 255, 255);">________</span>Untuk setiap <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAqauOtt24nyjWAm8DQBhngZXWyRKd_JWnH2m89HEUmyvtPBpX-jxKzy1ufRvgGe-BqKdWft3JPzBHurpR3yA_m2ey1C0xaqZB4p5gt6YkamSrWjjXws_Y8I-gnVk2jvb0yrW2P2ik8EeC/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394562729765995410" border="0" />:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXDgZ5h5ojzfnJMMq7N7mN4ZgcvyqIPLbzxxncG6xEknkyzQ8IHgnKrmkV0vqwsD20GPBAtf-YqEhSajvMfVeG4krdjrBCiwGflllREm3rjlqBkai7ZKxD075qAOlDEXkKYHWZcROZYtPD/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394855660467770242" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcsIjHFcen9D3pIJPR-n4jHVSZFttIKe0H_VLGt8E9PkafvgtAzC45ztWzRNQ7BrLdLzZA0HZdmD6SBgqZKBhK74MsTMvcn232Tw563W84WFa0JhMfrZXrM2zz6C68fYq4MM15AGluVdxk/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394855578976431730" border="0" /><br /></div>Menggabungkan keduanya:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4ZT9fnjW9DDQAzcI8mq0X9e1NuwUTET0zJakYWtU1-GtOf4WsHLbCTy5YKDvST-Z3jXaVF8x_hlirp9DZ18IhIWBKwUNWCDVRq9cH8HXdYVqw-jTCXE00Fz9a3F5KNaibl4E5_fntKIcg/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394855570511572642" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVxglzTMA9A8Pas0jPofuE5fKls-urWZM9nOlB58r6Lr8vqgmolOS9vZ0MZikXF0Ndk5QowILUhYdMwdb5djCIUpL3VMWZhJH6zb8ergiGvQVOAQeGGXH9wLO-dNui8ZAAHDxWoK1DUxar/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394855563356509906" border="0" /><br /></div>Sesuai dengan teorema keterbagian bahwa: "jika <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHs8FjJMCEv65NX6MdT8NgLfV8SawfxYDSsdO89czWgF9NR5hLl1HYj1RZZG-yzQm_PcJetUBHmguu3dTzG2EKZ6C4vuT49RPKhBOfLxDBLVa5E6vrYtYJINv_Rz_hUcneJmuT-tRIMb2-/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5394856642170015826" border="0" /> dan <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqof9sKOIIbMDC_u-S_nQ70LZm673Yvb4_8no4X4MJ15ePV6hYEsMqBJZwMPo1XJJjcjy4Mzf9LhNCMg7DMwESLJ_vKWz-XvrO64QUAOaTzUCs81hWfHlXv5wf1JoE0zoe6XG84Y_askW0/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5394856640223424690" border="0" />, maka <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmVFYYpsHRDx0pIzkSWNcu9hed53gAG53VQM9idwK1cvQUyM4N8chPNDQ8rvMcqG7Eba8-gTDG4gJ7wSdHRZRXJ4ophc3-xnZ5QWlDNbxrDl_j_kFet-AF5lZPOcBNqBuXlvOWvDd1B9Rc/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5394856632413210722" border="0" />", maka<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0yK1QLXQMpzEhl0sb5LYNG3yVzvrD6lRHpN_YH-GfOTqpd_sFT7D42EYt6N5pVzSDR22ELGNfM0zGd0jmHmmFOX_PIZtPz2qKWOf9Y8fLf57Z1TuPi-ZCFXUJEuG-X1hx1YLwt9zi3_ZZ/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5394855560405416338" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikGlQS0lqqdykvSkso_hJHVpPBsm7xvHABcHxuH9f-BgCy8xTpaD3AUMuQG0KboFkgmOIXsq_RXR2N3pNv0v6Hg_XdpS8a4Cs-F3gerrLhZhOoYm1HCR_idQo83MgTmGlTWRCTYs-JqcjM/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5394855549695334370" border="0" /><br /></div><br />Dari hasil di atas, diketahui bahwa antara solusi yang satu dengan solusi yang lain adalah kongruen modulo <span style="font-weight: bold;">M</span>. Jadi, solusi CRT menjadi:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7Z00WR1pUUhI7jLs4h95wyY1_huabBMML2XsNsZxWwFmPhngSleN0IxWTTT9-brvv73ACXGXL2GCSMk6qXVL1d1tjy6F8cJ3fY6dCcNbX1OOhtCmVQPDf2hmpKRy9PDckKry7qfnDuTDg/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394561371067336194" border="0" /><br /></div><div style="text-align: center;">TERBUKTI<br /></div></div><br />Untuk lebih memahami penggunaan CRT. Perhatikan contoh di bawah. Kerjakan sebagai latihan.<br /><span style="background: rgb(235, 78, 7) none repeat scroll 0% 0%; color: rgb(255, 204, 102); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-weight: bold;"><br />CONTOH 2:</span><br />Temukan integer yang bersisa 1 jika dibagi 2 dan jika dibagi 3<br /><span style="background: rgb(235, 78, 7) none repeat scroll 0% 0%; color: rgb(255, 204, 102); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-weight: bold;"><br />Jawab:</span><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSIqeCPi64HwSkOMM9kZ5LPyHuph9IYFrXW3alBE3Wx_djEwC_jFmNufbrJVObWOzwWXD6y881D40elaFGSYhNg_xW9fVuVQkb5h3mqiHYycyG6aEDW_p9-62wXv6YuR87ecF6zxkkJb-y/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394859229472379266" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgosqwriEXb45__FmoyFndgh23oPvde5x-g0w-HaIweLcB74pJUqrZ7UdzLq5XJHmBVhXRbWw7W2xVnAKvhLAEeSdDcMH4xz2zpEyGzrXzgCq3_SSu-IYdV42r_SJfOKkRs3HeI01A4HrZF/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394859225649005538" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwlkSmVi9pk6EBl79uVP02Vbl2GMPXt-2VJWILuh6HiUKT9gezIqO1YNp-sWBGd546Ry1U1Jh1WlyqCx1ZhA7oTBzEwcxB0uARjBTRJJwb2a_kRskYaAhFiicbwBWU8q42MBDDQObmTvaQ/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5394860664094043250" border="0" />, <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgU87yYQ_befFducuEzjBT4YkhuK7RKfS_Ervh0kjIgpdNy5WAl6x8dfxa7LDMitLTXz8KZ_z4Q4k7PG_8P9WcZFTn8cj1Uj5-IeYEPBYyVhyHkgo23dbppWU9dLt3yVToGOA2AMOBQdDJ6/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5394860659698301826" border="0" />, <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9sWiDEvOAgwa9IDB0PIOV4FDhbIClUjwZ302PUp8GWjgdXS3qgzkZASr1-wl_JZITxGwsV5-yK0hwMOQlQk7VHp3EkbRAj7XLfQzi1Oe-iVA4UObQUWLNv4-x2_MhnBZCtuULJ34h-PfD/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5394860310593521106" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgervnFkMY5mNMU-g2ar6D2DlAPvtcgw1q_iy67sui2YpuAA2cSoD1qZ3nI5EzsyQ5RFETW6w2Oyc8XI2NyUDaVKoQs_rAL9N2hpIow4I2QsFhip6INghPvcgdjaYRpAtKa0aPS_z4S1saM/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5394860305758377586" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEzIcSdYihfXBIC_q6U_eENjAurQIQyzZalC1tPoDgtUMLy1Lvf6p3KIhEnIDNwlNCdaTThVFcEQ67EzfUcEbFEPnfLcuTM4RAA48Xc0qVQeSWdfFVUnftnOqsOKOXFcJ3EuCjHXcB1Xu3/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5394860304631784546" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmuBAiziUtz5bA4VPEZr5YvXDya1ruYbQGKaR89Rb9kdFy4OzNtLDh_tAA4DvSLTke0tcuvnQqKyuch6gcNEXpv4UWLrbSHwAQPPSRiFQSd9y_cNcKT-mROqzD-oQvF-VkEaNXGcHL81hZ/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394860298612616962" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBbgaSiyA7q-5_VaF69VosHbrOymkTw1b2apMAhAcoQNPeo5OIkggCL5t7PuAKWgfKgtHx8JzEQw75NAkeEF7ydOB2AufCmgDBpnGi09sVmANpkswreidB0Z1PVrI_H0DszevvUBtzcP9w/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5394860293987304466" border="0" /><br /><div style="text-align: justify;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVBQzHwBxzNj9leOXSOY_-dxUjUsFjpYVeXQ4_Lmkp2bFzQcjHXVzXEdUKvJz8o92ZIUPDyi2keOo5Oda973lvVoWVjUi3Z1zDddXJny5YrBQ5ZZr_7AFxb5NAkOPl6jD-fjaIgN0uz5Ex/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5394861312791435266" border="0" /><br /></div><br /><span style="background: rgb(235, 78, 7) none repeat scroll 0% 0%; color: rgb(255, 204, 102); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-weight: bold;">CONTOH 3:</span><br />Temukan integer terkecil yang memenuhi<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqOjU1P-ryzu6MPezruSojP4aUhx6w1-2IvXzFBlwI3ykTUlpwxCquViEmqoWGODxCzrP83vbSiMZaZ9_anRnEJeJJONAdV4AjHTcZRAMuJZ9xyh_wMPenQ5qfhO0pZraGjKgquho7Lda_/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5395385264813090338" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLi5vojd0EXWcXG-gtNS-ijJBA8X1hyphenhyphenR5Ij-jxGXnAABq-NzbCC2rTcjgrNe6PvbEECMoawGYg2-Oz5VEzPcp9RBbk7WLKLDzR8isM_Hw4nhoyjNG0exrTULrP-EVYX8fEnEyVKa5T46mG/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5395385257615133810" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXj7qamCRKQ7zW44jzZSCo-Ky9S8F9N-gKuPWs83zXPYOIXoxDh4oGK0LUw4L4cO2PF0-t2jhhHaTXZwlOfstO2Ip8kU5uZdm_aIjwSpVECbQyHbzGV-pk-0vrt4cy3Y5fP4HGHO2chr-O/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5395385253904007570" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxwUTbnn4cAaDCKEkMpVOpyuk9H5feDVpnjyWzs2GZEWUsXxBwmZ2IPqALNxVrPu4gGNlZvXpAU5QwYgRxgep3SUT4b94XW7gBR5UP8-LsVmMOkwu88AOzktCsuZ3xnbh4irWeRgnvq_Ie/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5395385251977810594" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1nPCamM6zp_XqLfm6kY3QrJof90G4ji6eE_Rs0pglxn2HjJwzlmwE_x5kW2BHHwlCf9Ylu0BXfyrHJbBnAePL8PoqgSavrJvnzxsmXEEEQkSd488qJRbiAxXDvYx9029wvP5bF8VtMLUr/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5395385247611762050" border="0" /><br /></div><span style="background: rgb(235, 78, 7) none repeat scroll 0% 0%; color: rgb(255, 204, 102); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-weight: bold;">Jawab:</span><br />(Note: akan lebih mudah jika diselesaikan dengan komputer :D)<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjEf1uOk7vypHZh_jVW6iPZj-zdgZdWMbGq1p4kACtxSRXLJJgY2EvD4okNdeKacdkshtmsTbIP4xmogk9E1ycrIgBB7MrTnI8QWW_2gQWmJoQVfKAI4eauBmls_39v1pv_YfrfUl0bpIZ3/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5395387890263373250" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGioB6Hvn7PSRzRnkEmw-cXcaemVd38MO2nUuz1aWJG9bDXMuW3v5lxnfkcZ63QINn4W-2Cu6WFe7iIJTW8N55kw-47FjdlynAZzKGnjOekCKFp7498ypAqOTROOzUT6x9QdVzj0IRdgt6/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5395387815615158162" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh4iJ8z8VfkhdWd362aAvV3fXGWJ2WPPmWycp0AYwoXquL2xdlEd2YYhOSM-_MMKp4lmHJZ3UH4vrRzE-YZV3zMFkLh5ia86399CNVvvarltb6yucZUxOv7oJiGwPsY5BbB9pnDl8jqjrM1/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5395387808319235570" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrI_n8w3u8C7eVchdBM18E2BuO64WsqtKK2uVaT0JNTmkRxR92ziL2ABNu7XqieZLW3SwtIca1DVf_fow0Q8EVs7Bjih_xrGb9dwdG6GVdFc3Z8KTZm_nkmsMNBYRl8fmERbL8s8hIsFFR/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5395387806871239666" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTB9otDEnAC60pT1yQT_uyVcXCaYCOcwfIHuUDc2LQyBtm4BVlUExxlQ4TZX6hHNuQyXqUfww015zNoutFmLzgsAOO0R-yv3YprgV-Efvm1XwE1UMSRnOq-STIo5WI_9pzpA7ylXRnK2Zc/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5395387803005038994" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI2-DPXN3OeNRXnfuEvrZuVX2ZHjgiA0rcPFgGnmRJm7C9CMB-KQcxX9eZ1h_1L5gJFRY0Ikq8RLOgrXVcqOguR-jGKFutI3GMQso93rbB64VBrYj0QVR2BiFdr7rHD2X-YzXHG1rilLI0/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5395387798749988946" border="0" /><br /><br />Kemudian, carilah <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1g9110FbIv0zgm2AOq82az-bB_6-TPVPl9vEfJoVm-nR7iGdtGVpQKj3Rz9ffw1qRKvAI17aiODdlNUaXTs6uOA0VcMQxZ0H4v28lBAaOwFfCNN4Sz7wj6jGWM0gJ5IHOlB4FjULPjqBB/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5394562721103809458" border="0" />.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV-NvInnmEFXh_CAf0hMgAiVhQl02P_-T8YzVEJe4oG23qOTN-JCtIPFSPAREEWHl8Fw-A0A23PphhBBZFLDi_DpyyfSw-aUbt1IaH_1hXM_ZzvHqvRTSJNPdPWPwz9bM-qMZCtqmdB1e6/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5395390160815727506" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQAF6KLd73vac5i55oOqB-8Ne_jrXdqcqqZogDfraTgpD2mwzNtWFudKQY_baF45RAfebTFQiPVYrPJDyq44QiLB53u0RXx8HowywPeiM9nS5m3XnG7gHw7BieSoXrHV1_oA45sNCIqxAY/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5395390155160606450" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF2r3Rk6A6i7vQk4CFqehn7UGQDRnvyANDKHplkcMEXMsApcRiTj2qrZJqs7qmlkE2UbFYBFvxM_YL7jJi7JLDlmz8NIsfrZs4-6OPDsqw5i5db9PdTuB5qMbliR3z5oITAV_ixfAnLUI1/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5395394525365920610" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheWPaCZL5QtMm6YVMqQoPJRPGg6MgIGjeAedbyVWaIauyGMb9anK0FuOnUm1dtJHIz3LVdpReeYdLxVKHShBjliUGndOLrE4ej9I1WzwZeqtZcpyMqPX8CLO3BRV7D-4yvIRmfuQGoxhgy/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5395390149852935586" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6DtdnCKF_nenngzrAAjlNbCFcmImh_VWyI6Y6iogf8r8cywljw1fo7z-itEeVVt1GIIOMZXjUwJd6feb21NDKbqYAItunpQeDFQJfgLZKthS0OFARimI26uF7uYL7abMdpn_uz0PlwsQ2/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5395390147511508578" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS-5avnflcF0-vtAdxmC9gyH-ix_o5cG7HBJ13E4I-2yDURvX_LzT2AHJrPUk-7_LUVeUZ2b5-2ukBu_kgFtXjFfNRaFNsHsB_sZDmHY8hVOMN3NO54ytXRd6ZcQ7ENhtr-AtYwZPIJ4kb/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5395390142890690930" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjM7Iw6rDSmNDtwEnhCFcb_awYT489fuQdo1wiLpplmlgYsm8TS9vLiJrO8jvIyFKwPZ2MZ9SZ2MCQ8G-TROs_MJfoIvQCvUzgK6GUg7l0zOyM8imVpVZl1EuQ_4kxEN0DlnB10Hrr9HMHe/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5395389976478977746" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPs0uVYHPSO296duyXk7zz6ohr9Q9INJUm-FfsICTllHdogIw2PiXtJ8yOwUaCoSCrhky-qTgAqKKIs_AhXijphesE93Vpm4oK4tgnrMuYGXHU8kRondkuW1kd2YEn6jjO3f6nHjAUIuv2/s400/23.gif" alt="" id="BLOGGER_PHOTO_ID_5395394521116049858" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9o1Zcqx_ZOkAAS2vmAgNpBRQzccg4dAsy0Fa41Xicc1ACqXyzqmOwRp2hFOTYkYlF6H3iZddHzOrn0o56UCwtlKGM5PgGNUIIOsuZlYw1IGsK9kU-T9rQl_yCtmDj7WzqCNy8CSFHdYJH/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5395389966510775490" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWJlLSBF3KbDNwKR7gmgswvCMBIrc9LWB5GqZnHIxdl8DQq3YBRM2IEiGRMqBoz40E-FJPv8dh9wGyKj-EjA8Ii7RchAS2Z-8f_hZ7lGp8u-s-BDbjpmQimQ51YulOk6adberndIMLs1eV/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5395389966764737378" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ35lpuMNO4QLfC7HZeGfwGgGUkhf8sJvUADROztd1W_BXFK4m8lglUkDT1sRGV93w4xXCTqckHJG2D6-Kh2kpfpnt0HmDOaO-k4M12DE92GyqIMFtRo4sSfxeWB7E-1iDN5OvE5cmSTHS/s400/24.gif" alt="" id="BLOGGER_PHOTO_ID_5395394520950506802" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfWF2t_gUN9fRqDMDifgbbn9E_Az7zL6Wz3tUDRtZeGzm61nW-qnG5byZHjAsvl37U0Ery1q5VbPlb4d_VFgkOsHFgGRhRR-Dst4o6uxijYXpLY2JmaA1yvDCnE5f5jT7FJPj8gmtsHsRX/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5395389961792472018" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGol5xJGF4f7XdOnjQITrpVLjaFccc2xBzoDQfZN_otAlDnRT6k00Dy6OQyBsvgcxZGeV277KXqdIz8cLW46uJHe0oeJbynJu8Op6bzsr_M-kMMjKwzB7IVn-LwybgQcZVVkNCuqrmdX4I/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5395389959107532338" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaIZguH6kqLEArTMyYdvx_vdTh1ek5eTKBKlPvsMqvdQb9KO-fkaIekcf6Oqq4Hn997aXp_SS-wrGg5rk09MnTATNjfNxkVWIKqX0X4d8_Xxoumfr2_Xmhg_rNgs7BqsfUOqXwq2yTklyX/s400/25.gif" alt="" id="BLOGGER_PHOTO_ID_5395394520514491266" border="0" /><br />(Note: untuk mencari invers modulo, biasakan untuk menggunakan teorema Euler).<br /><br />Selanjutnya tinggal memasukkan ke rumus<br /><div style="text-align: center;"><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxsK5chaWmj0x9y6ldQkysHhGVoImOTaZtmqQUxj1ITqS88skL002mWvxatxCfAW-d8-4LwUR9czttt5GH3PwdgL2beZBGrL4c1Xf63twpyzmfLOJaAPr3ZdFMZJjV6Hy4bKhGdeGwSBMg/s1600/26.gif" alt="" id="BLOGGER_PHOTO_ID_5395397025385544930" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJjFlyzLLHg4qds_4qBhyXUmpNZD50AXqp4fTeiauRha38exxHCfpajzLCHwCLzWsQFudpAw9YeS1X8u58k6kvRtfSsBvUhhdiCwHBECS1MWu-TqS50tAoVDbBXinjaalWkm1KTBIYz8Bu/s400/27.gif" alt="" id="BLOGGER_PHOTO_ID_5395397022887986322" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhzkMbsrL5FlRMnJbO297vR0bPacYBEPHAxKoVshc7xaujs3fyXIpjqcLPWW2V5CtE7utynRl7xMv1oijJsaF45JYv5tV4A5vIvFaDukCf1ezoTaKnXK3j_JE9XchpmQQ501dNvrGJeVkt/s400/30.gif" alt="" id="BLOGGER_PHOTO_ID_5395400228982980946" border="0" /><br /></div>Jadi, bilangan terkecil itu adalah 150999.<br /><br />=======================================================================<br /><br /><div style="text-align: justify;">Demikianlah posting kali ini.<br />Materi CRT memang jarang digunakan dalam olimpiade matematika, namun aplikasinya menarik :D.<br /><br />Untuk memahaminya, pelajari materi dasar dahulu seperti keterbagian, modulo, dan invers modulo. Jika masih belum paham, tanyakan di comment atau YM atau email, bagian mana yang membuat kamu tidak paham. Key? :).<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com4tag:blogger.com,1999:blog-8125318493233557109.post-46778244593877149782009-10-13T21:03:00.002+07:002009-10-13T21:19:10.138+07:00Ikut OSN PTI Pertamina Yukk :)<div style="border-style: dotted; border-color: rgb(255, 100, 50) rgb(100, 204, 255) rgb(100, 204, 255) rgb(255, 100, 50); border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: justify;">OSN-PTI (Olimpiade Sains Nasional - Perguruan Tinggi Indonesia) merupakan ajang kompetisi sains di bidang Matematika, Fisika, dan Kimia antar mahasiswa tingkat nasional yang digelar Pertamina sebagai bagian dari kegiatan tanggung jawab sosial perusahaan (Corporate Social Responsibility/CSR) bidang pendidikan. Ajang berhadiah total uang tunai Rp 2 miliar lebih ini akan menghasilkan kandidat yang akan maju ke olimpiade internasional.<br /><br />OSN-PTI 2009 merupakan penyelenggaraan yang kedua kali. Pada penyelenggaraan pertama (2008), jumlah pesertanya mencapai 4.666 mahasiswa. Untuk tahun ini, berdasarkan tingginya antusiasme mahasiswa, total peserta se-Indonesia diharapkan bisa mencapai 10 ribu peserta. Apalagi, penyelenggaraan tahun ini sudah diperluas dibandingkan tahun sebelumnya.<br /></div><br /><span style="font-weight: bold;">Syarat Peserta?</span><br />Asal kamu adalah mahasiswa minimal semester 3, kamu bisa ikut. Gratis. :)<br /><br /><span style="font-weight: bold;">Bagaimana Cara untuk Ikut?</span><br />Cukup berikan surat pengantar dari universitas (bisa Kajur, Dekan, atau Rektor), terus isi formulir pendaftaran online di <a href="http://www.osnpti.com/">www.osnpti.com</a>.. Mudah kan?<br /><br /><span style="font-weight: bold;">Pendaftaran dan Seleksi</span><br />Pendaftaran : 5 September – 26 Oktober 2009<br />Seleksi Peserta Tingkat Daerah : 3 Nopember 2009<br />Seleksi Peserta Tingkat Pusat & Final : 4 – 9 Desember 2009<br /><br />Untuk lebih jelasnya, silakan lihat di <a href="http://http//www.osnpti.com">www.osnpti.com</a>.<br />Ikut ya, semua. Gak ada ruginya kan ikut lomba gratis dan berhadiah? :))</div>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com4tag:blogger.com,1999:blog-8125318493233557109.post-41171546099626900522009-10-09T16:24:00.012+07:002009-10-10T12:42:43.371+07:00Menghitung Super Cepat<div style="text-align: justify;">Di Toko-toko buku, seperti Gramedia, dijual buku sulap yang ditulis Deddy Corbuzier; <span style="background: rgb(0, 0, 0) none repeat scroll 0% 0%; color: rgb(255, 239, 57); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-weight: bold;">Book of Magic</span>. Harganya lumayan mahal, Rp148.000,00, namun lumayan bagus. Isi bukunya adalah berbagai sulap sederhana yang menarik.<br /><br />Ada trik sulap "<span style="background: rgb(0, 0, 0) none repeat scroll 0% 0%; color: rgb(255, 239, 57); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-weight: bold;">Menghitung Super Cepat</span>".<br /><br />Bagaimana memainkannya?<br />Sebelum memainkannya, persiapkan dahulu 4 buah kartu yang diisi dengan angka-angka sebagai berikut.<br /></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCwyXFTcBs_iSIwDFGwNhgU9HISh8a-ipmcYukrtxa25nwxWk_ddrc_SnKHRvTT-U5H_15bmSWOxX-iL7q3CgsuKNyV3Jiels3mI-PZE1mcMn2knNdpnUw4dAfmZCr09eU4D2VaiAJWbE/s1600-h/Kartu+Bagian+Depan.jpg"><img style="cursor: pointer; width: 207px; height: 187px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCwyXFTcBs_iSIwDFGwNhgU9HISh8a-ipmcYukrtxa25nwxWk_ddrc_SnKHRvTT-U5H_15bmSWOxX-iL7q3CgsuKNyV3Jiels3mI-PZE1mcMn2knNdpnUw4dAfmZCr09eU4D2VaiAJWbE/s400/Kartu+Bagian+Depan.jpg" alt="" id="BLOGGER_PHOTO_ID_5390823841959891810" border="0" /></a><br /></div>Di bagian belakang masing-masing kartu juga diisi angka:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIP40KZ5aMKL8PsLo5Zndtd99TXutrVc9zwuPt1ml3fDIvFuo1p7ienbvuPWmElcf0ArdRcvUW0zZdhOwRoUKuIt9ahhbEYwo9dcCxAnsNRzzz2UARQ43PHTuRYz6stozEE7iTYhkMP8Y/s1600-h/Kartu+Bagian+Belakang.jpg"><img style="cursor: pointer; width: 207px; height: 187px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIP40KZ5aMKL8PsLo5Zndtd99TXutrVc9zwuPt1ml3fDIvFuo1p7ienbvuPWmElcf0ArdRcvUW0zZdhOwRoUKuIt9ahhbEYwo9dcCxAnsNRzzz2UARQ43PHTuRYz6stozEE7iTYhkMP8Y/s400/Kartu+Bagian+Belakang.jpg" alt="" id="BLOGGER_PHOTO_ID_5390825551118547170" border="0" /></a><br /></div>Penjelasan: <span style="font-style: italic;">3 8 6 4 7 adalah bagian belakang dari kartu 2 2 3 9 6, dan seterusnya.</span><span class="fullpost"><br /><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh85Rx1D_O86WV1NYqS_a94e6v-_JNHo9uxifZHx_bAib1Z6-qNVTORurLphucSIyUT6DJUhk_El440I9mnCqK1ZXpaqCT6HotDhunzG4FmoQj5qY2w9embEXf0kPoosqJoElAdFKz82Ro/s1600-h/how.jpg"><img style="cursor: pointer; width: 326px; height: 35px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh85Rx1D_O86WV1NYqS_a94e6v-_JNHo9uxifZHx_bAib1Z6-qNVTORurLphucSIyUT6DJUhk_El440I9mnCqK1ZXpaqCT6HotDhunzG4FmoQj5qY2w9embEXf0kPoosqJoElAdFKz82Ro/s400/how.jpg" alt="" id="BLOGGER_PHOTO_ID_5390838275784118738" border="0" /></a><br /></div><div style="text-align: justify;">Cara memainkannya sangat *sangat* sederhana. Panggilkan salah satu temanmu untuk ikut serta. Dia bebas mengacak keempat kartu itu dalam urutan yang bagaimana pun. Setelah temanmu itu selesai mengacak keempat kartu, maka sediakan kertas coret untuk menghitung jumlah semua angka itu dari atas ke bawah.<br /></div><br />Contoh ilustrasi:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxg1oBK_1WYpC4g9gXGUBScLpjBa1ojfshKZ9Z1QTddfDWdpynuunStlPJILM8k75Nv-9YPJ23BSx25bp_Exs9gUy1vsv04RxYJ-O_DHobQ4I_ZucvlrZ4cgVQRkKk13nSdySjO0-57Ew/s1600-h/jumlah+2.jpg"><img style="cursor: pointer; width: 265px; height: 234px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxg1oBK_1WYpC4g9gXGUBScLpjBa1ojfshKZ9Z1QTddfDWdpynuunStlPJILM8k75Nv-9YPJ23BSx25bp_Exs9gUy1vsv04RxYJ-O_DHobQ4I_ZucvlrZ4cgVQRkKk13nSdySjO0-57Ew/s400/jumlah+2.jpg" alt="" id="BLOGGER_PHOTO_ID_5390835937206083218" border="0" /></a><br /></div><div style="text-align: center;"><br /></div><div style="text-align: justify;">Dapat kita lihat bahwa jumlahnya adalah 24590. Silakan cek di kalkulator. Setiap urutan yang berbeda akan menghasikan jawaban yang berbeda pula.<br /><br />Sementara kamu terlihat mencoret-coret di kertas, suruhlah temanmu itu untuk ikut menghitung. Yang pasti, bagaimana pun caranya, kamu akan dapat menghitung dengan tepat dan cepat. Bahkan lebih cepat dari kalkulator.!!<br /><br />Bagaimana cara (rahasianya)??????? Lihat lanjutannya di bawah..<br />=======================================================================<br /></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhabqyYNB_br5JukCkvvApN_RSsD4XsAYq7iZ-KE0ZNQbYfpSl8A8olsC_5xATdJ6P1elvgxhDYuAZxGCvug-DCHANbT5iu1Js49NNe37vsO3WLBspWELa7QzD8jerN2n-cr65RmxtS96I/s1600-h/apa+triknya.jpg"><img style="cursor: pointer; width: 307px; height: 35px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhabqyYNB_br5JukCkvvApN_RSsD4XsAYq7iZ-KE0ZNQbYfpSl8A8olsC_5xATdJ6P1elvgxhDYuAZxGCvug-DCHANbT5iu1Js49NNe37vsO3WLBspWELa7QzD8jerN2n-cr65RmxtS96I/s400/apa+triknya.jpg" alt="" id="BLOGGER_PHOTO_ID_5390839071125111858" border="0" /></a></div>Cukup sederhana.<br /><br /><div style="text-align: center; font-weight: bold;">Tambahkan baris kedua dengan 22220<br /></div><br />Dari contoh di atas, artinya kita cukup menghitung <span style="font-weight: bold;">22220 + 2370 = 24590</span><br /><br />Coba kita lihat contoh dengan urutan yang berbeda:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6ZA9BDQnXffmUPWpdo3Ku5p_7q9Yv7eAaB7owmCAStRsPxCIwzCuczzlqXF5RQFCTksU8rY1jHT43WWvYqkXGeVNS0U5qpppzSvUxVGbZaC_w204AX98qERhi5rlhv0u7yNmJH-fUfvg/s1600-h/jumlah+copy.jpg"><img style="cursor: pointer; width: 265px; height: 234px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6ZA9BDQnXffmUPWpdo3Ku5p_7q9Yv7eAaB7owmCAStRsPxCIwzCuczzlqXF5RQFCTksU8rY1jHT43WWvYqkXGeVNS0U5qpppzSvUxVGbZaC_w204AX98qERhi5rlhv0u7yNmJH-fUfvg/s400/jumlah+copy.jpg" alt="" id="BLOGGER_PHOTO_ID_5390834343725914882" border="0" /></a><br /></div>Hasilnya adalah <span style="font-weight: bold;">22220 + 2130 = 24350</span>.<br /><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Note:<br />Permainan ini harus dilakukan dalam situasi yang tepat. Anda harus serius. Jangan pernah mengatakan bahwa ini hanya permainan sulap. Jangan pernah menyebut kata "sulap". Jika demikian, efek permainan tidak ada gunanya.<br /><br />Jangan lakukan permainan ini seperti permainan anak bayi. Artinya, jangan buat penonton merasa permainan ini terlalu mudah. Oleh karenanya, terlihatlah serius menghitung di kertas. Tulis semua coret-coretan yang sebetulnya tidak berguna bagi Anda (hanya sebagai aksesoris). Jangan terlalu cepat menghitung. Sekali-kali kegagalan juga diperlukan untuk membuat efek dramatis.<br /></div><br /><div style="text-align: justify;">Mengapa harus ditambahkan 22220? Siapa penemu urutan ajaib ini? Mengapa bisa demikian? Semua pertanyaan ini tidak dijawab sekarang. Ini juga masih menjadi pertanyaan bagi saya. :)<br /><br />Terdapat <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0zDWvKApO4H69SiLTNS6NwAxU3qIbvvKb5Gyao-IgAEw0gcydGyjs3eRka-yQ5qwsE92Z1ccw39prTY-XrdVpLM6SjgFUPhCNDaeRpTXFXAURPlnTPjHU97PddG9qTkNTzm6PwvYpdwc/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5390841873484810722" border="0" /> cara untuk menyusun urutan kartu-kartu tersebut. Jadi, akan mustahil untuk menghapal semua jawabannya :)<br /></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber: Buku BOOK OF MAGIC oleh Deddy Corbuzier.</div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com6tag:blogger.com,1999:blog-8125318493233557109.post-23595056282592544752009-09-20T13:04:00.004+07:002009-09-20T14:12:14.082+07:00Kumpulan Soal dan Solusi Olimpiade Matematika Tk Provinsi 2002-2009<div style="text-align: justify;">Berikut adalah kumpulan Soal dan Solusi Olimpiade Matematika Tingkat Provinsi tahun 2002-2009.<br /></div><table border="1" width="100%"><tbody><tr><td style="font-weight: bold;">Judul File<br /></td><td style="font-weight: bold; text-align: center;" width="18%">Ziddu<br /></td><td style="font-weight: bold; text-align: center;" width="18%">Rapidshare</td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Provinsi 2002<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576919/OlimpiadeMatematikaTkProvinsi2002.zip.html">Download</a><br /></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282464692/Olimpiade_Matematika_Tk_Provinsi_2002.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Provinsi 2003</td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576920/OlimpiadeMatematikaTkProvinsi2003.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282464925/Olimpiade_Matematika_Tk_Provinsi_2003.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Provinsi 2004</td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576918/OlimpiadeMatematikaTkProvinsi2004.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282465152/Olimpiade_Matematika_Tk_Provinsi_2004.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Provinsi 2005</td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576915/OlimpiadeMatematikaTkProvinsi2005.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282465469/Olimpiade_Matematika_Tk_Provinsi_2005.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Provinsi 2006</td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576923/OlimpiadeMatematikaTkProvinsi2006.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282465872/Olimpiade_Matematika_Tk_Provinsi_2006.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Provinsi 2007</td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576922/OlimpiadeMatematikaTkProvinsi2007.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282466118/Olimpiade_Matematika_Tk_Provinsi_2007.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Provinsi 2008<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576917/OlimpiadeMatematikaTkProvinsi2008.zip.html">Download</a><br /></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282466531/Olimpiade_Matematika_Tk_Provinsi_2008.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Provinsi 2009<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576921/OlimpiadeMatematikaTkProvinsi2009.zip.html">Download</a><br /></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282466759/Olimpiade_Matematika_Tk_Provinsi_2009.zip">Download</a></td></tr></tbody></table><br /><table border="1" width="100%"> <tbody><tr><td>Kumpulan Soal dan Solusi Olimpiade Matematika Tk Provinsi 2002-2009<br /></td><td style="text-align: center;" width="18%"><a href="http://www.ziddu.com/download/6576916/KumpulanOlimpiadeMatematikaTkProvinsi2002-2009.zip.html">Download</a><br /></td><td style="text-align: center;" width="18%"><a href="http://rapidshare.com/files/282469251/Kumpulan_Olimpiade_Matematika_Tk__Provinsi_2002-2009.zip">Download</a></td></tr></tbody></table><br /><div style="text-align: justify;">Kumpulan soal di atas tentunya tidak terlepas dari jasa orang-orang baik pelatih olimpiade maupun peserta olimpiade. Mereka mau berbagi solusi dan men-sharenya ke publik.<br /></div><br />Jangan lupa mengerjakan sesudah mendownload. Jangan hanya dilihat. :)<br />Lihat juga <a href="http://hendrydext.blogspot.com/2009/09/kumpulan-soal-dan-solusi-olimpiade.html">Kumpulan Soal dan Solusi Olimpiade Matematika pada tingkat Kota</a>.hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com7tag:blogger.com,1999:blog-8125318493233557109.post-38128953414944634422009-09-20T12:31:00.006+07:002009-09-20T14:13:47.370+07:00Kumpulan Soal dan Solusi Olimpiade Matematika Tk Kota 2002-2007<div style="text-align: justify;">Olimpiade Matematika tingkat SMA dimulai dari seleksi tingkat kabupaten/ kota, kemudian provinsi, nasional, dan terakhir tingkat internasional. Kita dapat menyebut OSK untuk tingkat kota. OSP untuk provinsi. OSN untuk nasional dan IMO untuk Olimpiade internasional. Tentunya, olimpiade sains ada banyak bidang, termasuk matematika.<br /><br />Tentunya, untuk bisa mencapai tingkat Nasional bahkan internasional, tidak ada jalan pintas selain belajar dengan latihan dan latihan.<br /><br />Berikut adalah kumpulan Soal dan Solusi Olimpiade Matematika Tingkat Kota tahun 2002-2009.<br /></div><table border="1" width="100%"><tbody><tr><td style="font-weight: bold;">Judul File<br /></td><td style="font-weight: bold; text-align: center;" width="20%">Ziddu<br /></td><td style="font-weight: bold; text-align: center;" width="20%">Rapidshare</td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Kota 2002<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576703/OlimpiadeMatematikaTkKota2002.zip.html">Download</a><br /></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282462129/Olimpiade_Matematika_Tk_Kota_2002.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Kota 2003<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576701/OlimpiadeMatematikaTkKota2003.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282462573/Olimpiade_Matematika_Tk_Kota_2003.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Kota 2004<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576702/OlimpiadeMatematikaTkKota2004.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282463159/Olimpiade_Matematika_Tk_Kota_2004.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Kota 2005<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576705/OlimpiadeMatematikaTkKota2005.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282463365/Olimpiade_Matematika_Tk_Kota_2005.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Kota 2006<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576704/OlimpiadeMatematikaTkKota2006.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282463521/Olimpiade_Matematika_Tk_Kota_2006.zip">Download</a></td></tr><tr><td>Soal dan Solusi Olimpiade Matematika Tk Kota 2007<br /></td><td style="text-align: center;"><a href="http://www.ziddu.com/download/6576700/OlimpiadeMatematikaTkKota2007.zip.html">Download</a></td><td style="text-align: center;"><a href="http://rapidshare.com/files/282463668/Olimpiade_Matematika_Tk_Kota_2007.zip">Download</a></td></tr></tbody></table><br /><table border="1" width="100%"> <tbody><tr><td>Kumpulan Soal dan Solusi Olimpiade Matematika Tk Kota 2002-2007<br /></td><td style="text-align: center;" width="20%"><a href="http://www.ziddu.com/download/6576706/KumpulanOlimpiadeMatematikaTkKota2002-2007.zip.html">Download</a><br /></td><td style="text-align: center;" width="20%"><a href="http://rapidshare.com/files/282464488/Kumpulan_Olimpiade_Matematika_Tk__Kota_2002-2007.zip">Download</a></td></tr></tbody></table><br /><div style="text-align: justify;">Kumpulan soal di atas tentunya tidak terlepas dari jasa orang-orang baik pelatih olimpiade maupun peserta olimpiade. Mereka mau berbagi solusi dan men-sharenya ke publik. Jadi, jangan terima kasih ke saya. :)<br /></div><br />Jangan lupa mengerjakan sesudah mendownload. Jangan hanya dilihat. :)<br />Lihat juga <a href="http://hendrydext.blogspot.com/2009/09/kumpulan-soal-dan-solusi-olimpiade_20.html">Kumpulan Soal dan Solusi Olimpiade Matematika Tingkat Provinsi 2002-2009</a>.hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com6tag:blogger.com,1999:blog-8125318493233557109.post-32529610122130631442009-09-18T07:53:00.055+07:002009-09-20T11:44:19.492+07:00Teorema Euler(Pelajari dahulu <a href="http://hendrydext.blogspot.com/2009/09/teorema-kecil-fermat.html">Fermat's Little Theorem</a> dan <a href="http://hendrydext.blogspot.com/2009/09/mengenal-euler-phi-function.html">Euler Phi Function</a>.)<br /><br /><div style="text-align: justify;">Fermat's Little Theorem (FLT) bekerja dengan baik jika bilangannya adalah prima. Namun, hal ini kurang memuaskan para matematikawan karena kurang praktis. Bagaimana dengan bilangan komposit?<br /><br />Tahun 1736, Leonhard Euler berhasil membuktikan FLT. Kemudian, 24 tahun kemudian, FLT digeneralisasi oleh Euler. Selanjutnya generalisasi ini disebut dengan teorema Euler.<br /></div><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 50px; margin-right: 50px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;">Teorema Euler<br /></div><div style="text-align: center;">Untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhR-QWuUAmhccN9HYp1oMtti5oti_wXKA0yMIG6RPws2_jT4MsLvVklacqtzBDNw8AjzVXM9ION5a7dSJ6Q2pfqei4x5drBMEDTyJ2GuTep5fPyaO1rvWteLrigdKqIm6VkYn5S9FJ-yP0/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5383121988768374354" border="0" /> positif integer dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaMCWapbUyMcMo8wLy6TVM0MNJkW4rekJE-7IOwI6uXBsk8NqQ1sZNPgoPovHsbuURRfmdPUmIbD7UNOKAz3litJSsKFQ3k8DuEkiLzUelgfi9AeI2etPUllrK2aTd4QbnZiNBUJWOIZo/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383121985647482002" border="0" /> adalah integer dimana <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOl2ipaEqqtWLgNc31EkVEBXRn8bxop9swhtkG7pRLghm55eLwJ9LeWvlF5ZtFy5X-4a_qBcbMH619-pOayPjeCFbX2rrupQ4flTUbkj0N58Ek5w-T66nE07H_v9sidOybHlc5ctODhus/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383121599190542002" border="0" />, maka:<br /></div><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgal86QieOlpfOwCKPfn7ZuaSq_eTZf-Q7aoyOfwbmV908k5rIiUFJcUfugX4hJ4ornsiLZkG2zbs0xIsiBcuSY1KbW-FCzYI4j79526VC3rvZr4o-ZHk7wIQ7vj40Fij84l8JgfUKkqBw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383121593190712034" border="0" /><br /></div></div><br />Perhatikan bahwa apabila <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhR-QWuUAmhccN9HYp1oMtti5oti_wXKA0yMIG6RPws2_jT4MsLvVklacqtzBDNw8AjzVXM9ION5a7dSJ6Q2pfqei4x5drBMEDTyJ2GuTep5fPyaO1rvWteLrigdKqIm6VkYn5S9FJ-yP0/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5383121988768374354" border="0" /> adalah bilangan prima (<img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYbZ30TCeuUMU0kBZ-7okjCFEaxssV2BVZvjLJevDE8JRff37LTJKZMSY7E-6V6RioqeRD8OBnbtg4mAdNhwxKPVekjGn1VASKKCCKMTRHQbpF2zTtKB7vhvrq_OCxOT_nXCrkXu8RDjU/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383122810273029346" border="0" />), maka FLT berlaku:<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzNE_uUtQuVPNyCld_4qtignbLcYiwa0_belwAEEk1iwV3fOfRcqnAk0sogX3_cD03X6oXIePWrK9375-UlZHitjtN5r-gykckVTid_Jeua0rfRzMn8nW6oh8HvSMD7MUcS5wV1ZhFqOc/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5383123484670170274" border="0" /><br /></div><br /><div style="text-align: justify;">Di post ini, kita akan mempelajari bukti teorema ini, sekaligus mengenal kegunaan dari teorema Euler ini terutama dalam menyelesaikan soal kongruensi modulo dengan cepat. :)<br /></div><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivBPyoJJ09Y9EcbBibGOtt6I43YiESt3CH7TceUvvY-Ja2GIVYDHBbUet7-FuEHjwfiQQdCalKBjrHCaAqHNd0ulOBlBEZBZAJr2b5NKUh8Mmq5xhDlW84Lg62GAAS97oHB8WEB5uUxVo/s800/1.jpg" alt="" id="BLOGGER_PHOTO_ID_5383128824788034898" border="0" /><br /></div><br /><div style="text-align: justify;">Konsep yang melandasi bukti teorema euler adalah <span style="font-weight: bold;">sistem residu yang tereduksi</span>. Perhatikan penjelasan pada kotak di bawah.<br /></div><br /><div style="border-style: dashed; border-width: 1px; padding: 5px; background: rgb(171, 244, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: left;"><span style="font-weight: bold;">Sistem Residu yang tereduksi</span> (reduced residue system) modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" /> adalah kumpulan <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_ouEVvEUnAF073nZIl9OmAYFj8JQP7pXXMdieYOdkkgAg2mFxJXzfurcHOC9YCIE0P0jaTDM3BZkjtRH06nocWC9g_3tjlSiVVrbDZADMgGhBzxJPn3udY-6bBpsg5wZfAXv8bOkjbT8/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383143420523251106" border="0" /> bilangan integer yang totatif (koprima) dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" /> dan tidak ada 2 integer yang mempunyai kelas sisa yang sama.<br /><br /><span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 1:</span><br />1, 2, 4, 5, 7, 8 adalah sistem residu tereduksi modulo 9.<br />Perhatikan bahwa <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5Ee_P4ZOG_mSPBmGew_-zCmsBSqaCHEdkOpBYPQMhptmo2VmOgz7YRmH8HLvGP7Mvso43JUH9rn9dIWBC7bNZjaBFBPwqEp0dJOe1cIX7cy2OkILEnnpM0QTgP51oJOZ6T9FwXHb6Df8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383144924828419250" border="0" />. Jadi, jumlah bilangannya harus 6. <img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh55-LCkJ3Astj7dJlEZ66I37iPT1JwcdZgO-gsS08LlmyeMkhUGbpp-sgoShxbiY7bKAd11qkU2GJxGCb5B3Kkj-1tt0_AxbrcUkl9hnZmtqZ9kT3Qehiag-lhgwv2uBYJSGsXzyOERNY/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5383145251678351938" border="0" />.<br />Perhatikan juga bahwa bilangan-bilangan itu harus koprima dengan 9, dan mempunyai kelas sisa yang berbeda satu sama lain.<br /><br /><span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 2:</span><br />-5, 7, 14, 19, 29, 35 adalah sistem residu tereduksi modulo 9.<br />Perhatikan bahwa semua bilangannya koprima dengan 9.<br />Tiap bilangan juga memiliki kelas sisa yang berbeda:<br />-5 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 4 (mod 9)<span style="color: rgb(153, 255, 255);">____</span>7 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 7 (mod 9)<span style="color: rgb(153, 255, 255);">_____</span>14 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 5 (mod 9)<br />19 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 1 (mod 9)<span style="color: rgb(153, 255, 255);">____</span>29 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 2 (mod 9)<span style="color: rgb(153, 255, 255);">____</span>35 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 8 (mod 9)<br /><br /><span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 3:</span><br />1, 5, 7, 11, 13 BUKAN sistem residu tereduksi modulo 12, karena jumlah bilangannya ada 5, padahal <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgtTz5zDKMZG0_1PizNgbcBumu0ZuLUcP887-w0zmLdghrXE0bAC4JovnbJ38RTCGjPOO57A4W7e4WOsAD03mU9QszzD6BRHd5qDHBsYtCKWv_zcrnjALHCF4QbhJH_Scspi70R7abYcg/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5383148216534583330" border="0" /><br /><br /><span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 4:</span><br />-7, 11, 13, 17 BUKAN sistem residu tereduksi modulo 12, karena<br />-7 dan 17 memiliki kelas sisa yang sama.<br />-7 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 5 (mod 12). <span style="color: rgb(153, 255, 255);">____</span>17 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 5 (mod 12)<span style="color: rgb(153, 255, 255);">_</span><br /><br /><span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 5:</span><br />-7, 11, 13, 51 BUKAN sistem residu tereduksi modulo 12, karena 51 dan 12 bukan koprima.<br /><br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(171, 244, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 20px; margin-right: 20px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><span style="font-weight: bold;">Teorema</span><br /></div>Jika <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEib4EBNhtz3SMwISygsWqeCZ096RH5IieN-M6OTXrT_sUIYePUEA9e0PiAp3o_Y1cEb5Kn6FF_ks1PmkdRHR_wUcefRzDWI3PM3d7vyN00Gs3R8_7LFQvEHxvHFFF7kUKPcdDhKNEThmSk/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5383151126491879234" border="0" /> adalah sistem residu yang tereduksi modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" />,<br />dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhT-YSSpUGNBrQMDXYE1O9h2ERk9z0x1wTHBmTtoklvohyphenhyphenHXt7RRZnexkRGLLWBUbtVfBWQts-MnpJ5gLhR0OxMUvkDp11QezJ0ZslB12G9UrrWDoyt11N8A6cQ-l6wjLfUfqhNJjdKW98/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383175012499185122" border="0" /> adalah integer positif dimana <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJGEK6I4XB33zRqxceIEifhH-FnX9S44F8pF85UZi2MCG2QFFu5WXgYK_Fc6pdQxTi_Lh5of5sSoKITRMj6r6U1wdsDUlGsK4116gk1KfN1487Zl8YEEOimTkhaSAUi4D280R0hyphenhyphen0ObGE/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383175461952305490" border="0" />, maka:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh34UP4Vt5RrqUXaJZe0nspvLF9_yyjYo0inQOM-G9ABihCfbL-8gzYNzeyxA-llxd9BkyPBkS04RGFODmn6W8zK7AVX7t-bXWTF_Qymv0wol5a1RpaOR9i13EuuUDl3v3gezAgcDp-nV8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383175780685091474" border="0" /> juga merupakan sistem residu yang tereduksi modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" />.<br /></div><br /><span style="font-weight: bold;">BUKTI:</span><br />(i) Bukti bahwa tiap elemen <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAPQrDUrvn9nfy7x2zER4y-2ErxZGZSvKyGKvLg9cttKZun2Ze0vSfZi60-EptFRxOws6dHEDT1fUu7UjBEQleEdEnkunLYwo7SrQGRKAceYNa2OxHsTmcb0YOxBuQ5pWEwMVkCvAD5JA/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5383176294885232770" border="0" /> koprima dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" />.<br /><span style="color: rgb(153, 255, 255);">__</span>Karena <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJGEK6I4XB33zRqxceIEifhH-FnX9S44F8pF85UZi2MCG2QFFu5WXgYK_Fc6pdQxTi_Lh5of5sSoKITRMj6r6U1wdsDUlGsK4116gk1KfN1487Zl8YEEOimTkhaSAUi4D280R0hyphenhyphen0ObGE/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383175461952305490" border="0" /> dan <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJnFsIjIyTWSuq0SyXIuzvtPkcxGlF0cdKxVAxz19AeHlqEzga1aoXfOh0bSNCKeW3DSPAWIAK_BTSJeA1DpuBhcIv7ayNNcQCLH35DznpRJJQPHeqUKfq-WTdKsrX99smLMmiwGpAK8I/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383176864416761106" border="0" />, maka <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMjuDvKUCr1a2u2L6e8UV7cZ15CrsYEAv8QOmLcaTcE1qvy50DJoHIOUPqPSmpwEfM7tsqMuERMzdQgZUidUleVuuFwCPbnZjFO4g2lN42t4PRx-UjaVBggmoP4OoIRUF9PBcVydjYqMw/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5383176857799538322" border="0" />.<br />(ii) Bukti bahwa tiap dua elemen memiliki kelas sisa yang berbeda.<br /><span style="color: rgb(153, 255, 255);">__</span>Asumsikan bahwa ada dua elemen, misalkan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkjVCjqwysvtzMoZMS5MyyUMgDU1fxTtCi2pXkwSCv0RowCSfGMwPErswK66RS74fYArE0nrC4YLmEC5wO_vo2MTFmz2ZzO3ZaR-KE1eQbXrcuIe6blR_7JLT5bzL4SyLI-bPK7MYhMUg/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5383177561640158130" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglovevHFH3Mw-A_H3Vi-TNVBQJKrB7ucyHTHMhw3KQ0SPjml86XFk1wrdBrs8eEq1X0kBqZ0KMctKAAYMaejjNsYNr-MijBpmjF8SbydvKSQ8B9o_qNcu6N3w5DOCpFxh9rsQyTHx6IxE/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5383177557557430402" border="0" /> yang kongruen modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" />.<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQbvznlRa4nOZyCZl6VEJxHIndSNzyk2QY4FUqXMTofQkWCDVhFlSiUvI0lpuWd1an45nUGABNInqv2Q9O7-D2pR7fsIsdEUDWuDQ_bnMvlfBvWd1gbbEFANBORecwP4pJFuoyQ5I9lNw/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5383178944098546674" border="0" /><br /><div style="text-align: left;"><span style="color: rgb(153, 255, 255);">__</span>Karena <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJGEK6I4XB33zRqxceIEifhH-FnX9S44F8pF85UZi2MCG2QFFu5WXgYK_Fc6pdQxTi_Lh5of5sSoKITRMj6r6U1wdsDUlGsK4116gk1KfN1487Zl8YEEOimTkhaSAUi4D280R0hyphenhyphen0ObGE/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383175461952305490" border="0" />, maka:<br /></div><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNk_tT-VT-7PuDojHgWI8Hnv3TLHykD7MZK1b07XAdgkJLaOHVOsEC_x0xbY57lfNEp6kstvyPdqRY-AZUMjKucGFbLzRqGDGpwZ4DtdiDHmGjUCNtMaodFN0xo7vaF5lfrEbxQWZQif8/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5383178705840308562" border="0" /><br /></div><span style="color: rgb(153, 255, 255);">__</span>Namun, kita tahu bahwa <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNty3wAciGWjD4PEQnDCXNYlRg4_3oTwdDW0pK0jmU8MxYFc_6pnK2YAKe1_pA9-LEQD3BAJeYroJQNNP9tbZx277IM50VW4ERCTJN-K0KzHl6T6TBBQ_CqvjC67f7FuUo-kObtkAvdlQ/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5383178698558785698" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTMRzjxl8Umv64gCFp8sTZiY3ruCs2xWP0dea47-x8yzLdLDT82mVNmHCOXvYOt4W4MTGvwb3cxGt-s0iuuCmPQaVORAZFQ99KK1jjMJ1kR2uLAMzUy4e1-zSBL-vCJGmInoy7B-T8e5c/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5383178692127762962" border="0" /> inkongruen (karena keduanya berasal dari sistem<br /><span style="color: rgb(153, 255, 255);">__</span>residu tereduksi). Oleh karenanya, kontradiksi dengan asumsi awal.<br /><span style="color: rgb(153, 255, 255);">__</span>Jadi, <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkjVCjqwysvtzMoZMS5MyyUMgDU1fxTtCi2pXkwSCv0RowCSfGMwPErswK66RS74fYArE0nrC4YLmEC5wO_vo2MTFmz2ZzO3ZaR-KE1eQbXrcuIe6blR_7JLT5bzL4SyLI-bPK7MYhMUg/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5383177561640158130" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglovevHFH3Mw-A_H3Vi-TNVBQJKrB7ucyHTHMhw3KQ0SPjml86XFk1wrdBrs8eEq1X0kBqZ0KMctKAAYMaejjNsYNr-MijBpmjF8SbydvKSQ8B9o_qNcu6N3w5DOCpFxh9rsQyTHx6IxE/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5383177557557430402" border="0" /> yang inkongruen modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" />.<br /><br />Dari poin (i) dan (ii) dapat disimpulkan bahwa <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh34UP4Vt5RrqUXaJZe0nspvLF9_yyjYo0inQOM-G9ABihCfbL-8gzYNzeyxA-llxd9BkyPBkS04RGFODmn6W8zK7AVX7t-bXWTF_Qymv0wol5a1RpaOR9i13EuuUDl3v3gezAgcDp-nV8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383175780685091474" border="0" /> juga merupakan sistem residu yang tereduksi modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" />. ■<br /></div><br /><span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 6:</span><br />1, 3, 5, 7 merupakan sistem residu tereduksi modulo 8.<br />Karena gcd( 3, 8 ) = 1, maka:<br />3, 9, 15, 21 juga merupakan sistem residu tereduksi modulo 8.<br /></div></div><br /><span style="font-weight: bold;">BUKTI TEOREMA EULER:</span><br />Didasarkan pada teorema sebelumnya pada kotak di atas.<br /><br />Karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh34UP4Vt5RrqUXaJZe0nspvLF9_yyjYo0inQOM-G9ABihCfbL-8gzYNzeyxA-llxd9BkyPBkS04RGFODmn6W8zK7AVX7t-bXWTF_Qymv0wol5a1RpaOR9i13EuuUDl3v3gezAgcDp-nV8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383175780685091474" border="0" /> juga merupakan sistem residu tereduksi modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" />, maka tentunya sisa residu positif dari <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh34UP4Vt5RrqUXaJZe0nspvLF9_yyjYo0inQOM-G9ABihCfbL-8gzYNzeyxA-llxd9BkyPBkS04RGFODmn6W8zK7AVX7t-bXWTF_Qymv0wol5a1RpaOR9i13EuuUDl3v3gezAgcDp-nV8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383175780685091474" border="0" /> adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEib4EBNhtz3SMwISygsWqeCZ096RH5IieN-M6OTXrT_sUIYePUEA9e0PiAp3o_Y1cEb5Kn6FF_ks1PmkdRHR_wUcefRzDWI3PM3d7vyN00Gs3R8_7LFQvEHxvHFFF7kUKPcdDhKNEThmSk/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5383151126491879234" border="0" /> dalam urutan tertentu (acak).<br />Dengan mengalikan elemen-elemen tersebut, kita dapatkan:<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiF0kzzli6R5kXHCQqOrUrPKMmxRGwAJGabuAKdkE9ibZuZRreEY-gPRFa5fO6EnExYNSSFMuxLrH04EHgLkuuIlYrivnnneHYj4RwZEABa7pGBjs3LCcFYORmsZapdrJ2-6M4ADqe2Tp8/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5383183664427446850" border="0" /><br /><img style="vertical-align: -8pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheDqIy315_NT0qbw6AKaTggI3sBrtRgpiE7cHOED4lnhsTA-oi_A-ig-A0BpDVSolwCRJVVafMdWVT5om1a5ZBmIx_WCfXvMKFciiRl17_mtjhd5atliApxwP7V90y4IdWRJMLO2DzsJA/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5383183655811229074" border="0" /><br /><div style="text-align: left;">Karena <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX4jTiXlcEawjDESWDlSbG2tHABKXCS3dOetsoNHBll-yJTWXue5c12oi7PytfjxP4BBHpIP1zBsqY2JbMDiUkBx4w7fbtMGVkvFCHpeA5A8MEXnLNFGrZqJKP8nCzB2vaH7NtqG0YCek/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5383183652284983458" border="0" />, maka<br /></div><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiruzMl_R-YZNw3DR_zEcdBODDvTipG3ceeJ5HVSBDLv4_8RFwxdQcXXGZWSWdVOHb7h5nTAnDp5YFiMDEw30DePzxaByoLQrMMM4PY1Nfnl07aJ7RbTYFRUPBQWy7Cw-7SwxrZnOel6YU/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5383183644646169698" border="0" /><br /></div><div style="text-align: center;">TERBUKTI. ■<br /></div><br /><span style="font-weight: bold;">ILUSTRASI BUKTI:</span><br />Dari <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">contoh 6</span>, kita tahu bahwa<br />1, 3, 5, 7 merupakan sistem residu tereduksi modulo 8.<br />3.1, 3.3 , 3.5 , 3.7 juga merupakan sistem residu tereduksi modulo 8.<br />Dengan demikian:<br /><div style="text-align: center;">(3.1) (3.3) (3.5) (3.7) <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 3. 1. 7. 5 (mod 8)<br /></div><div style="text-align: center;">(3.1) (3.3) (3.5) (3.7) <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 1 . 3 . 5 . 7 (mod 8)<br />3<sup>4</sup> (1. 3. 5. 7) <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyQVH6PJu5DmPrj6U5YOKdrhCeTSAAj3eTce4acyzw_LxVl1rQBzhoTAnDBDfxJ4l7i6zs97QAzUdgQ00pya5mIl297uUYHEPcMgrqdJ0-8QmkeozsbF2YD4qqAJxZeDNM0ZXHGC4W5Zs/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383146594353551922" border="0" /> 1 . 3 . 5 . 7 (mod 8)<br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUJFehCmAR55eanYJ7mUS65X3r4EjgNwaOMGbjQNASxloDm-kr0pJVAjAVoGfF9Y4vCT-7BIUsrCrkTlByNipuCnwvk4Yp8zbO9Gxn9RTE-HtajkAWasxOtZo6SViMQ6ST-zbmLohD8nA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383207565728440722" border="0" /><br /></div>=======================================================================<br /><div style="text-align: center;"><img style="vertical-align: -9pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaBIlfI20Ln2nKJSYMHOZDx3zuqPITTW_woNLaRnwhE6G0yDbz5RxqejqV7S45D7_fGBZs2Rwpc0qyt0qZXN8eZ9prvu1WykFUgRWj2-S_c3CfLrrsKydNwIGV7IShPb-gzvWw0wQ7nL0/s400/3.jpg" alt="" id="BLOGGER_PHOTO_ID_5383131302911809746" border="0" /><br /><br /></div><div style="border-style: ridge; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="background: rgb(255, 200, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 1:</span><br />Tentukan digit terakhir dari <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHJZJ7TqjKaqfpS5Z9NKJgK07v8qiY7oAB8pc2v8Fuo4AUIUitD_VCbPBM0hHJinI-Yhp_gOY-R7QmAhu1YRnWtnuCGGe9yJr88L_1xtVkh19nRrRvpWglerHMzizszn2S-57bJ6iNSok/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383219962187679890" border="0" />.<br /><br />Jawab:<br />Mencari digit terakhir sama seperti mencari sisanya juga dibagi 10.<br />Sesuai dengan teorema euler, maka:<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_crNrE2KcVIJCMAQcmC1I5KoYIBZkRMqLUQ9be2dSawuXPpdh8IdV3H47ort0eaAR-vrtDrJvHXra4Se463Z_4jMyLvBxQeqdwD-f7Gx76afyP0h-2kKcgnDA9CChui5s7nWXgqBEQTU/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383222974946286242" border="0" /><br /></div>Jadi, kita kelompokkan berdasarkan 4.<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1K8pFm5D2eQO6OfPuBxFXw1O8C4fYpxok-FGF1SD1xL0eSVDIfom8GOXeU6Euf5ntgZKt9GNyjARzf_btBkRMj6zKpWIPC-ZfRdUZGtAg4qZInXg5TWiyktbHDkdBtizvJ7g21vmnf9o/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5383223830953499266" border="0" /><br /></div>Digit terakhirnya adalah 1.<br /></div><br /><span style="background: rgb(255, 200, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 2:</span><br />Berapakah sisa pembagian jika <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxpuH7MHqWmkpTmzRl3A6BFYBZhWBdDJXkXKhflPIDKgthdUpS-cU4RuYJNCIvFW3i6NY1eiBAMcq0GBmlAjXVuBdQ5xxBl5hXf9P4dKY8st5UuPt6jACIvwmWiTctk_PwZVvVqJ6HwJ4/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5383225017666478146" border="0" /> dibagi <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYTPDSocY1NKI-vojc33VtYHZnzEeW_LiiLBUAVNdSrVLt3sNehepYnYVAebap-3DdWJSDdEKXm8uVvuqgcw95wglNqN82-PsE0ij77i1fZ4COetEgkNckKbfiT172jHGT7QtuMidYGGA/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5383225013922388018" border="0" />.<br /><br />Jawab:<br />Sesuai teorema Euler,<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSLzlZFEjlYKlX9daG20J1i_LXF4z-C1Pnn2w7fK76n3bBTEg7tlyLlXz-fwRnTfOq-BjZkjO9-vBnErtLBAIPJz23xRT-kePj1bIxnDrK0wa2jplavWQBYyZqk9fTw4rkIy-JTQlKRTA/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5383225847041533762" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOOTlXljNWf_XKNtTuLdY6Ow9J7QReiMShk5moD21bILo4KYpe4z_JlV0S2OkuREPra0BfZmzvar1YdM2oNHJ37a9HQ5aB4feXW1JgPP_LdVFAL5BJw8SXZS4hRR294pfg7GY0elOZxwQ/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5383225841629085890" border="0" /><br /></div>Maka, kita kelompokkan berdasarkan 24.<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIPVOvpry4DyhqxV0OT7oBn2qzbM9sWxv48sM10y1m54Hc7E-SQdpHlkvXqzTWmojOVW0zrMvEIfo9Y4Hkv9VcTODVRyyF7D6xtLGfTdRpffjDzAWsd5XpWhRj1H0g6AZwUE9MYt5KpRI/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5383226899456514370" border="0" /><br /></div>Selanjutnya, gunakan cara biasa:<br /><div style="text-align: left;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMxF4oh45ibpeZP5HjGG1AYdNNkA1iI3UTcPiGKE_njg1DBB1FJ9hSzv9sl-nCU-lqgmziOSiPpfRDMv8RbSUfh_pHNCrGvhe4w0SueM21eAmAvXF4Zc_NH1n1dd8lJFIL7EiNuDkrr_c/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5383229518522658882" border="0" /> <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBJy_otV2DcoMohaFrJ2nYdIZyiW-2XLeQlwT_fne_ItVZOS_c7p5RrxJ9LZMBXcU2q_Wxm1OezUrpsprsaEiHjAhLwGvn5bnRg5HPAXdjCm8-HPRSahGNrrTTLYn6jCcBYdo8D8-zqdc/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5383229093922036482" border="0" /><br /><span style="color: rgb(255, 255, 255);">___________</span><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhq2Tq3TxJQfL_GA438KhIkAKFyfJe1XBA_nl1bXI-Jtju0GaJEsRj-OCN5ELoKthQjeMUW8gfGMl22ByhCFFPtDdIwoJYhkt69qe_xVQEY8ogd6VavVhd8qojqUuUB_Kry_WcF4w5n6sc/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5383229086761097810" border="0" /><br /></div>Jadi, sisanya adalah 11.<br /><br /><div style="border-style: ridge; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="background: rgb(255, 200, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 3:</span><br />Tentukan solusi kongruensi dari <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_FzQyK5aldyoS-W_2-l4-tP5TrKWpEuxTDpPXHO0fydH3QA9XQZdgkLwOL27iapzmF8opZUfPJCXb1L5CeuqeDHTnXGZWtmkOdb01lVmefzAJPB0Qu_oRATaIh_LCpmMfWhpkyiat5Qc/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383387594307727394" border="0" />.<br /><br />Jawab:<br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 30px; margin-right: 30px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Teorema euler berguna untuk mencari invers modulo:<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrrSZCPOrWrAVGcBfyCxe6G2V3AljxGPPcldUVJThPaiE33dzS_mN9uTBpBzZuXDlkLDPkyPjgYxZsJoRYpYg-_M_cVTsyBG0HADvN67fYdxhet4FIYLmNnylcln-_WoitTze3YEuLoho/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383220979708278946" border="0" /><br /></div>Berarti, <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVZt3I26hi93R41J2aosgZjPXXtqmHf-zkVMVhV_-3JHmWylas3YzoTqmmnq_XIykDv-ZI3M8K56KNt53EwATVlPe31LmflocjWpqXlOYCaTbTq8RCG2HdIJuSmmfaBNoph-6VOzLmtn8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383221211663462082" border="0" /> adalah invers dari <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLWSKEZfSlnyzDThG1OZtIi2NP2Fp2CiK4Dxi_YxIRgGnxAvTNJzQsoZb2yer8XkSl8OndRACAuTYsw7zM593gASIexFfu2Nd-cIpZtTmCxp9k7429wxi_Soab3y4xBXG6ytm0HfTKHPk/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5383221463055163794" border="0" /> modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyWrmyvxHAAmF3UMYTGVmQfs7_SxNdneKl3qIOXzLravyErklwmKZTl5a8HBLm7lWdLH3craQD-8MGvlrIeq3tH1iceVhrlI9vIPe43uRY3js8AfBi40WNqF8wx8t644bnvegnxmpaKnY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383143033898549122" border="0" />.</div><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrGtFNWFLsgYDeYZhUE-UUTu4n4w0qa70LxnVlK5NFIj68IqTMcT_QjnIS_E9DKRKv43pzE00MJnba_fhp-rWu8n67rahBYPlP-1K9-A3xYmcmMQHKX12ytxHgVLpK5KPda-Bf5lNDxIE/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383389763589822098" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfRwx77PffPV7t2xm7rKIfPV4i2JK2p-38tAjDXQa_nbKoZMYUuQQr4_MK-ddlvsQpd5AZR22uNYwDVhGf5cfre0GlxmwlExc9f2zOZ7bLabcjd5r5fFYwL2TI0QRD5GGE1sWkr5B7RHk/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383389585184113410" border="0" /><br />Dengan demikian,<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizgRA3IHjDLzpW8sOLwAC1v8atzF8lWsxFDC_llStz7fO4j8F8jRsy1afEZN5eq-81AAmWbR6RB66o1QF775Rg4xS0cMux4cMy0SjH5epz-iWID2V1J3XWo8JuCZprliJ_RG4i7vp43Fc/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5383389580796588178" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSP2Y3bOrTH-kmR3o3zu3CMOynTlVTfeJA-RiOjl5Naw4Iwmx6KQABVrlWWvy5ZvOLEIGzViRe97S-6OPmLQTnRfnUpszhL9kYFRPH0eRB07SeqrrJAWRFwKd2x-zAVVQJ7SOJMut-Ahk/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383389576502727090" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMOv8bwXy_8JvfRbJeUuo-AqUEpS-0fqVvXwwXe15r-QxDoSOrILojdq4vjTgGwgsjvjqY-WKB9mLivOn3tTRswwmS63JdUOiVUMco8mIpO5injbzdQ9BsnNmKwbW3OjsAc1dqF25-6cs/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5383389566102430002" border="0" /><br /></div></div><br /><span style="background: rgb(255, 200, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 4:</span><br />Jika <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirX5rr-HjiY3pVcQfbIHOE6HU0cnWJuc9S7donn8ph5_1VXbO2PNCjdyc117sQTLs6yON299xe2JTLBro16tmnHkZy668gvAuSR39JXLIfSy_IP0UvwrBeWPkiPiLNpOmSOFn-aNdoWdw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383390624987892002" border="0" /> koprima dengan <span style="font-weight: bold;">32760</span>, buktikan bahwa:<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpDqfnrt1AAS_-kzU3Tb8NS7etbGRdiWX5OylJm-aBmc8yaZa-1LhLQ7DjAriIKTOXRNenI9vlxZ5XdhsEnt8RCQYVriryHDgMm4jAJ7dqMsGbE_S7ZqcHmwS10kXz2kWKFSSQphApdsA/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383391085426008930" border="0" /><br /></div>Jawab:<br />Perhatikan bahwa <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3HZ1j2e0Baem2Ln8SSESF-TIicw2zqy7Lp2cWJDGDus86OC7JqSRLxseiip0HXcaBuybAft1IeRgvMLW7wwyOEUAjb3OSJY1OhkoHqzPlW9zGUvz7fiXmK-pp-aWNpgHQFG2hqkfS-F0/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383391708564428722" border="0" /><br />Teorema Euler menyatakan bahwa:<br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh38ZGomKrF0Zy7Xl193Zg4Nq2L-Sk86oLYw1zTGKblTLSAQzQp_chyphenhyphenufRFMqZxs11sBKm6fundaLO4k50mxhakRIRhdjS9dbEfbi8kEpBFv9OlY-YrBcqEVXUZNJGmunn54fSIu9ujtVQ/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383393374216698690" border="0" /><span style="color: rgb(255, 255, 255);">__</span>, maka <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMbfwuHzSoGzpP0e2odkb_MulwwafIcuTM_5-NegXwHrV8db8EL1PcrohwWTEv9sSjPLc2pVTRP3Ri1wDfYQRSb-WvFggazEVnyStAuKnBMEOc9lUSesw2eNHVTgop4yQngp5TNtn1RCE/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5383394491777624162" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-davswvigOHt4Gr_O6mU1iH3Ay59lDZxQ9dx3q5Io6YQpdshRkSoHVwfg3WWyTFUs8m8l0tAzdD2kEPaVpn8bwLa5Hv7YhqYgWsnwpTLHnwY7dq_oeewJi4Z9gK2WaSUXEZL5bm8h3fM/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383393371745909762" border="0" /> <span style="color: rgb(255, 255, 255);">__</span>, maka <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhv8f27exjvSQXoy8X32GuLB5TcnvCfgyyzkygNo_hosBrWasBQoVG29FeNKH6DTodd0wjumhuKk9Lvw2O52D_mKcA8hEuP-h3uIRj5GSZhCtRzt1plEV8M-GoIA5PYAkuDzQ70icEpm0/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5383394485979019394" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyNjIIXpaHCEnfvkgg7EGWw0dTfZ_M8OnEX8ASGQthqeeoqG0GjEhL3VX-Icr7Mzqs4p5R4sVAEsLQC24gOCDhyzR9wo7EV3gzZBDN9jsHe1OA6kUBmS9ugp2BGKR5LNLhYbXnEdEsnD0/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5383393360769697410" border="0" /> <span style="color: rgb(255, 255, 255);">__</span>, maka <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8h50C7-hxfRR8drDyFjWgI8wlJmd1UiSexiqg3anovA_SmuwO9Mn6S0OX7k9LXCPYfM5mNverb74gEK6HsX7FjgzXXdpvLBCVgGKCoHbjs3uT4pPJ5aWmriNmwFdYgSxr966Hh1U_cI0/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5383394476748748802" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7xnwd72ndHDPB53gz-dURBLYXrDjM1KqKomDKxpRDmJU8tKNqmfT0RRw0udaNL0aPjtnKDKt5OuM9qsyi_ENXdHkSigvymBkCvUiqeJXF2a2D8WvwweJdtIabFeY-1KWc2u7gAsGYvLI/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5383393352803503154" border="0" /> <span style="color: rgb(255, 255, 255);">__</span>, maka <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjufQVF1JuClq1-rE7E5sfAWl6WUzblQpLrRN1rcPs-opqY4MbAisQh8vXePwndQcqKtUCuMKMMZoVwJDv2WeFLTWVdUrr-t9AA76Z6t2NNjxNHhd6asURX-qPIxR8tCgFX50R2uQlDFK8/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5383394469504321762" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiw43wPaW17YqzeVCkvJA1N4PtW1CHfBoDRMWz9ScftqZC3iK18nG9lmm2-ulvOy_s6VuCK_3AX-3mHZnwLEVv2a9IbN5m-MKO_9uHjLVSEMYnAcctX_P34G05MhEA0Nn7jm7_cuxy8Ruc/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5383393348097176578" border="0" /><br /><br />Karena 8, 9, 5, 7, dan 13 semuanya koprima, maka<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpDqfnrt1AAS_-kzU3Tb8NS7etbGRdiWX5OylJm-aBmc8yaZa-1LhLQ7DjAriIKTOXRNenI9vlxZ5XdhsEnt8RCQYVriryHDgMm4jAJ7dqMsGbE_S7ZqcHmwS10kXz2kWKFSSQphApdsA/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5383391085426008930" border="0" /><br />Terbukti. ■<br /></div><br /><div style="border-style: ridge; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="background: rgb(255, 200, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 5:</span><br />Jika <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirX5rr-HjiY3pVcQfbIHOE6HU0cnWJuc9S7donn8ph5_1VXbO2PNCjdyc117sQTLs6yON299xe2JTLBro16tmnHkZy668gvAuSR39JXLIfSy_IP0UvwrBeWPkiPiLNpOmSOFn-aNdoWdw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5383390624987892002" border="0" /> dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4cqDllg0pDF2ZIEutL8me421ALeqR9NeJKlgC0WZIZi6KcfVaCQm-M7BJtiNCxSi1IOmcz7Qwtr58_r-fOwzFrLdJrJOaW0IxeEXkWFnlv25Kucd0JNDI0Iq2gZkwOLA333_pMRoWjMk/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5383396299960785250" border="0" /> koprima, buktikan bahwa:<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkn90JrzbawM4c-1C4cWWEVAumIgNps_S2qHLPMRJPXtMw4bcL9bA0D97-Dr4IzS6Ydsn3iVcLQJsTZZs6OUzgTWpIWEQha8ehXs0WmTZjcxkaTBbPhj_yd-bnjehQtOtRrwLVU4lEy6E/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5383396942066488562" border="0" /><br /></div>Jawab:<br />Menurut teorema Euler:<br />(i) <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFQL05wKD9gxjK3MSs4IvWBj-VUuf1QRuCIY59MUbytI6XqflHMfBVzH-aE2ZUi_IinokdR2t_YSPpQPYBmsnvF2_HPl6sovVJHq3HYiR9QuA1oml1qfcjFIafv1O_NNYuw-_DQDbkfM4/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5383397617712221874" border="0" />, maka <span style="color: rgb(255, 255, 255);"></span><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIi_vSu-aeF4cbP3mc4bvH8rJCu9FLqgDFM4xrAuYihG9bjcRybxaBcJMRqCyp3__tXKaZD1O1HVYL4s8lMoevwoToCvNs0BgETp8GFRB53C4JJARfQEVf6Fu_ml-4RReM_pTur_a3wrg/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5383398024720246082" border="0" /><br />(ii) <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVqczdumDytvmRkXX9NgNEdbX6_Lqu1CikfYWjpQVbNivQHIDyYlH1fPjQNjPkCa_Awe4az7h-wyBsoLsdUdqvYJgeruNr8fgooGSTA1bDH_KdhhNTYS389y3J7FSSEOIaAWG-K75M-hQ/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5383398703985033666" border="0" />, maka <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikNoTJuGLpur-oCFDVwOxfLKlF7M54UOi5kQRV92_V9Z7VseyhYM8LiHSwQPEEQWbHN4UodYPy2xCCDdIyvlvQTsYfT27E84M48USxCCqgqVPSLJNAhcrX58CswKvmGHtH7dfcdT_qS3Q/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5383398694686546962" border="0" /><br />Sesuai dengan sifat keterbagian,<br /><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAigu9LF8Z3q6IJX1lokEJxXKI1y8MEFhXlP5KFPnmeGFHPzGdGKH6pflJVvBFKGoI77crjeX0aGBSS6ulrJEIe85KlMywGR6MyfppONlKHqW2-lBudN4IMa9ogHMo4mF89gwgVOqUq_0/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5383400125151923634" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMr2x5dezPX-2gtpKHliMp9wjykxNVrysaQUfVWK18tMCQTbHT1Bko4JWAWSr9txEL8zpGYzyjci5RSIs0RU2v2ahS70a1qtqMKOJMJJyMvaENKQKhGVVs83tHTN9vezOheX139THwONU/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5383400118147784866" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-f_Fg-g9rUBK6rpemy5s5CxNLB0YRkJ7qb0FzYcZamPvKakNPjPnbIIzzopVOa546h-b64ZW7XDPDRhPhhvZ4B_cd3MtwTZaWhDhbaHTWpdZXyoi9BprbnDDggVoLT-_xHhtnR_yZS-o/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5383400112806672290" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn9ZSRn6WzsQr4G8TldQP-pJNCumasrrXHQPhEZyJvt9nDBiRDRflhuN0TgmU3n96IuXXpLZDs2sQnOKcmh2JNDuDWwA6x8UEMU01duQhUXR7bnW6MKt3YRKDrZXAsT8XN4TQKrtv3i3Q/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5383400103700193650" border="0" /><br /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgc6oZWR2JvjQrGxFsetStqbokQGEcv6hcEcgW56UBinjLqRnGSLEx_o_MJWiRXBtFz3hOcKYMSJwSgrmwQp8Q21O9okxkwnWhcSTgVJPZ8wWDBCee_Nr7LynuF8zjiqEeOPLiIZ01rrRw/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5383400099568410274" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkn90JrzbawM4c-1C4cWWEVAumIgNps_S2qHLPMRJPXtMw4bcL9bA0D97-Dr4IzS6Ydsn3iVcLQJsTZZs6OUzgTWpIWEQha8ehXs0WmTZjcxkaTBbPhj_yd-bnjehQtOtRrwLVU4lEy6E/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5383396942066488562" border="0" /><br /></div><div style="text-align: center;">Terbukti. ■<br /></div></div><br />=======================================================================<br /><div style="text-align: center;"><img style="vertical-align: -8pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1iKjx99zk5mu5zVHN9kN36TVddOfjcAsvQbZ7zuta4qlHOnFNB0q2_Sn1jXKJO5PAHvPhjexjjIsnDMC59pLU42t_OsKCmGSPmdPRwZ3fyBevRcKsCF-3iCExZIFgYzqgu3SQIYxtWfc/s400/2.jpg" alt="" id="BLOGGER_PHOTO_ID_5383128818323175458" border="0" /><br /><div style="text-align: justify;"><br />Di post ini, hanya diberikan perhitungan-perhitungan dasar yang melibatkan teorema euler. Dalam prakteknya pun, perhitungan yang melibatkan teorema euler juga merupakan perhitungan dasar seperti di atas. Teorema Euler berguna dalam banyak hal. Salah satunya untuk mempercepat proses enkripsi dan dekripsi dalam kriptografi, sehingga lebih efektif dan efisien . (belum dibahas sekarang).<br /><br />Dengan teorema Euler, kita juga dapat membuktikan formula eksplisit dari <a href="http://hendrydext.blogspot.com/2009/05/chinese-remainder-theorem_08.html">Chinese Remainder Theorem</a>, yang memungkinkan CRT diselesaikan dengan program komputer. Namun, hal itu masih belum dibahas sekarang.<br /><br />Tunggu kelanjutan post-post berikutnya ya :)<br /></div></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber:<br /><a href="http://en.wikipedia.org/wiki/Euler%27s_theorem">http://en.wikipedia.org/wiki/Euler%27s_theorem</a><br /><a href="http://www.cut-the-knot.org/blue/Euler.shtml">http://www.cut-the-knot.org/blue/Euler.shtml</a><br />Buku Elementary Number Theory oleh Kenneth H Rosen.<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com6tag:blogger.com,1999:blog-8125318493233557109.post-19687715713638470422009-09-15T18:33:00.057+07:002009-09-20T11:45:54.202+07:00Mengenal Euler Phi-FunctionEuler Phi-Function sering disebut juga sebagai Euler totient function.<br /><br /><div style="text-align: justify;">Dalam bahasa Indonesia, kita dapat menyebutnya dengan fungsi phi atau fungsi totient. Meskipun fungsi ini memiliki nama phi, namun fungsi ini dalam perhitungannya sama sekali tidak menggunakan phi (<img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRTsn7DCawzfBqBDZ8o2zaqzLtoFZEA0v4k0tXei1W3bAd-zgMcJWBwTl18atzX-poD979tCV13EE_WNXdbxaB-BjKBSqyZxHShQgjJx8Gn3s7_7JPCn3RcKbnH5XktcR2mW_KHXl7BFc/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5381661338915426610" border="0" />) yang bernilai 1,61803399.. Sebaliknya, fungsi ini hanya memperhitungkan bilangan integer.<br /><br />Alasan mengapa dinamakan fungsi phi adalah karena fungsi ini menggunakan lambang phi (<img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRTsn7DCawzfBqBDZ8o2zaqzLtoFZEA0v4k0tXei1W3bAd-zgMcJWBwTl18atzX-poD979tCV13EE_WNXdbxaB-BjKBSqyZxHShQgjJx8Gn3s7_7JPCn3RcKbnH5XktcR2mW_KHXl7BFc/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5381661338915426610" border="0" />).<br /></div><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 40px; margin-right: 40px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;">Definisi phi function<br /></div><div style="text-align: center;">Phi function <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8l5U_AHfW2nUDCGj23g7-d0UJhyphenhyphenY-9US3vi54wLMpsLtziHUI4hzIzoXBhFBNh0t_3pqvQRB0G17t5-yYKf38c4ZcTXQ442F0isCVQg_FH9WAYHJ81Sqx-Ak_vHbxRaYeQ5eOEK5-Jv8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5381663184909137362" border="0" /> adalah fungsi yang mengitung <span style="font-weight: bold;">banyaknya</span> integer <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheM0sWkmSl1qTP30kPhCAA5l2MP367IvCusy1Ye9L-EKgyXL-1tDjGmvOK2a07JyTmHxWoj1Bz1aps6zj-HQmOx5gNlqAFGY6s7LnmdXQYeaQHmVZ0NqvOZGohhZvojbzD_EIIUIxawmM/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5381663175589412690" border="0" /> untuk<br /></div><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7WGiO2hkpJTQREEmXr8EbY5EQY7jJK_1c66XZlT7eiEbRtCyDdoPajBMQH8Y35JvGN0g0IMtMSNIdn46pi9nZPPBNtJnCgSpXQo6CAaHKAz-BmW-0X1czA9wvbgoY-hx9i-xL38SLs7w/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5381663170206775426" border="0" /> yang memenuhi syarat:<br /></div><div style="text-align: center;"><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheM0sWkmSl1qTP30kPhCAA5l2MP367IvCusy1Ye9L-EKgyXL-1tDjGmvOK2a07JyTmHxWoj1Bz1aps6zj-HQmOx5gNlqAFGY6s7LnmdXQYeaQHmVZ0NqvOZGohhZvojbzD_EIIUIxawmM/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5381663175589412690" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0eveBtrmeEp-ExcLUOcLwQYorK5DTbq6GrWY8Rsc4P8RR3TzmyJIKHt6Hv37dR5O0PUwberFmJDYzPdV0pmTP3fD9gHkPEQ1eNgVtCJFEBbwz2hOcKimq25iSwPNtW_mtbS3Ov99hpzU/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5381663155682915810" border="0" /> koprima.<br /></div><br />Note, <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheM0sWkmSl1qTP30kPhCAA5l2MP367IvCusy1Ye9L-EKgyXL-1tDjGmvOK2a07JyTmHxWoj1Bz1aps6zj-HQmOx5gNlqAFGY6s7LnmdXQYeaQHmVZ0NqvOZGohhZvojbzD_EIIUIxawmM/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5381663175589412690" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0eveBtrmeEp-ExcLUOcLwQYorK5DTbq6GrWY8Rsc4P8RR3TzmyJIKHt6Hv37dR5O0PUwberFmJDYzPdV0pmTP3fD9gHkPEQ1eNgVtCJFEBbwz2hOcKimq25iSwPNtW_mtbS3Ov99hpzU/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5381663155682915810" border="0" /> dikatakan koprima jika <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBHcWZBzQWC8hffceWG6axNVIesjOFFzCROlfP_Yh7B0e5sFBaIat3lRAC-QZ3DsEdjaOQHUDKfoTEneBAzxWkAHs0vj6ofq_HCB1o3ot4VDJHM9exYlGweIXaaLJNMaHGNWIZQDAcueU/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5381663163090780114" border="0" />. </div><br /><div style="text-align: justify;">Bilangan integer positif yang lebih kecil atau sama DAN relatif prima dengan suatu bilangan lain yang diberikan disebut bilangan totatif. Oleh karenanya, fungsi ini disebut juga sebagai fungsi totient.<br /></div><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN1q_ESTxbzEgqDhoqYqqhweOh38L5njJR3-cBisqsVHRMJaF5Ib8KCQNZg9rEC1PLpN4y46BYNu6ijC90d4kY9j6JIFaTn2A2jRK6Sp16Mapsi6HebXoMZeQRTfw5gv8FYfUgIBWsfqs/s1600-h/judul+1.jpg"><img style="cursor: pointer; width: 240px; height: 25px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN1q_ESTxbzEgqDhoqYqqhweOh38L5njJR3-cBisqsVHRMJaF5Ib8KCQNZg9rEC1PLpN4y46BYNu6ijC90d4kY9j6JIFaTn2A2jRK6Sp16Mapsi6HebXoMZeQRTfw5gv8FYfUgIBWsfqs/s400/judul+1.jpg" alt="" id="BLOGGER_PHOTO_ID_5381681729311310498" border="0" /></a><br /></div><br />Untuk lebih jelasnya mengenai fungsi phi ini, maka sebaiknya kita gunakan contoh.<br /><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 1:</span><br />Sesuai definisi, maka<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_E80qHmXVeM0vcUqWW6hK-Ts7do_wZ-qSaZjLicFGU0z53i_WO2_rHbjNapu5FjA0AeITHfSU3DEGZqZZwMjqDheUes7Pw5XDbIt7Lq8KbkKqS82PlS5ktx5CYBp2Z2WiF7N2TB5FitQ/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5381685379133904082" border="0" /><br /></div>karena gcd(1,1) = 1.<br /><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 2:</span><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQZouTF-VJPZAdwMS6Gqu07dg7v957yv_lJGu98DwQghEWMePtY7S08kbcKBuVR48oeyghSW4S_6C05er95Ks35uxZNsX8eBd4Ry5tb38cryGLQhR1W8vuHV6vx94PXRSQRG8OAfuoliU/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5381686827458546242" border="0" /><br /></div>Dari enam bilangan: 1, 2, 3, 4, 5, dan 6,<br />terdapat 2 bilangan yang koprima dengan 6 yaitu 1 dan 5.<br /><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 3:</span><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtofwckugbYhj2MpTop7iFcKjgHB1KJXTQ_maFkoaY7Enj7tuUQGy6B9_ob7m52eRi_JhfVNspjYMfzyawrY8Y8BlDi_L4ihNtjCqjs-J5Jm8H3GGb-bMRxRMcNO4xfdvbjkFGM3toHsA/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5381687916769683042" border="0" /><br /></div>Dari sembilan bilangan: 1, 2, 3, 4, 5, 6, 7, 8, dan 9,<br />terdapat 3 bilangan yang memiliki faktor dengan 9, yaitu 3, 6, dan 9<br />Jadi, terdapat 6 bilangan yang koprima dengan 9.<br /><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 4:</span><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyzaMypkk4e4-Gu5qnf5mttxBS0BE7bJCVK3V-VYqkT7CV5Y4EC56gB3uE6VyO0Zyu2MmVF0OUfuSb-9P0-6usjQe7Vw_04SO1dxaTXUs0vdCSBgvHJbaQZQzqUpuvs14L1CmWiulSV1o/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5381688699821217682" border="0" /><br /></div>Dari dua belas bilangan: 1, 2, 3, ... , 11, 12,<br />terdapat 8 bilangan yang memiliki faktor dengan 12, yaitu 2, 3, 4, 6, 8, 9, 10, dan 12.<br />Jadi, terdapat 4 bilangan yang koprima dengan 12.<br />Dapat dikatakan juga: Banyaknya bilangan totatif dari 12 adalah 4.<br /><br />Untuk bilangan-bilangan awal, kita dapat membuat tabelnya sbb:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKxTuleNT1RqOEZhQsajV0BjS4vRJywh6rPprEXZxw3mAptqw2x4VNYV_aKB5tPz_F7j8Ih1t-8C9ZhAfRgrA9xly7vu6_CqslmccmNRlPS9DXOb2nXcR98t3Dri3NLcQYAk0-ZeOHsq8/s1600-h/tabel.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKxTuleNT1RqOEZhQsajV0BjS4vRJywh6rPprEXZxw3mAptqw2x4VNYV_aKB5tPz_F7j8Ih1t-8C9ZhAfRgrA9xly7vu6_CqslmccmNRlPS9DXOb2nXcR98t3Dri3NLcQYAk0-ZeOHsq8/s800/tabel.JPG" alt="" id="BLOGGER_PHOTO_ID_5382104839564248962" border="0" /></a><br /></div><br />Sekarang, kita akan membahas property unik dari <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8l5U_AHfW2nUDCGj23g7-d0UJhyphenhyphenY-9US3vi54wLMpsLtziHUI4hzIzoXBhFBNh0t_3pqvQRB0G17t5-yYKf38c4ZcTXQ442F0isCVQg_FH9WAYHJ81Sqx-Ak_vHbxRaYeQ5eOEK5-Jv8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5381663184909137362" border="0" />.<br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 100px; margin-right: 100px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><div style="text-align: center;"><span style="font-weight: bold; color: rgb(0, 102, 0);"><span style="background: rgb(24, 87, 198) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(236, 252, 223);"><span style="font-size:130%;">Teorema 1</span></span></span></div>Untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvjltDT-qi076Xs8WJ53Edm_CBAKtRC7APzqBSS4ogLtLMSsWKghJBT8O516nuuiJZA-I_m3CQRJUhWGXdp5VOyeSO7ZrcRJ-DEdJokJe_pTsBTpXUxVjLT_0TujcqGXYVOfRe5pHbEXA/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382106220582816850" border="0" /> bilangan prima<br /></div><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7jkW1Mk3_Qn9j1Vn06wl6qVULPuthoilXjiOqnOOof9MDcR7nio3TdDMa-dz-omPk2Dhqp4wgappN2kun4r_AfjIX8V3Ooufwid6j2B1dVmrSmQCfBMffsL5ibg27D9gs_nI24frBzDU/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382106223671781378" border="0" /><br /></div></div><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;"><br />Contoh 5:</span><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjeuKKL_fObsjcNe9lyOhICnbmVpYEi7ksVwritQvl4rwwBiBOtwp6dBP7HBSoSE67p2iuWA6B0-Ooyj1-cfcW6SSr2nVyDF7tPGeSwPz3B1wzGOkHO-FiptLRIo8OdT1m1oJoVOMKjmjw/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5382110675921697314" border="0" /><br /></div>Dari bilangan 1, 2, 3, ... , 13<br />terdapat 1 bilangan yang memiliki faktor dengan 13, yaitu 13.<br />Jadi, terdapat 12 bilangan yang koprima dengan 13.<br /><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 6:</span><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXkFIK3ZsqMnkUh6_EcUHc8uiu3nUEI4SbwGQyUNbFYFXaoSEkipht8GajB704hBbqgg3lzG5ZXMLIfb0PmLlXqT1WcH1MIwpEzO72z3Z3pWwrEAJ7sNIZKNyJhTEpHgmXRwg5mw_Z4zg/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5382112204496825986" border="0" /><br /></div>Ingat bahwa 97 adalah bilangan prima.<br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 100px; margin-right: 100px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"> <div style="text-align: center;"><span style="font-weight: bold; color: rgb(0, 102, 0);"><span style="background: rgb(24, 87, 198) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(236, 252, 223);"><span style="font-size:130%;">Teorema 2</span></span></span></div> Untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvjltDT-qi076Xs8WJ53Edm_CBAKtRC7APzqBSS4ogLtLMSsWKghJBT8O516nuuiJZA-I_m3CQRJUhWGXdp5VOyeSO7ZrcRJ-DEdJokJe_pTsBTpXUxVjLT_0TujcqGXYVOfRe5pHbEXA/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382106220582816850" border="0" /> bilangan prima dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhx-aHQaaTOHu6pC31A3Yq-LjeSwCJkZaRmrL_A4X5WlRtZU4GsOzC3I0m6r1QQxsdRp590jTsuyXHxao8fF3_viIzoaENj2QSdnIrOasT0oo8PmNorY5RjW1Eh7aalA9cInABEtLi912Q/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5382108767337603154" border="0" /> positif integer<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixX1EWvZL9aKtMJWA_G2WwSjZfXyVKBCum4z2uLM4mIWoNYqKW1-eUfbWXVh3kGr8ijYopFr7MDTQqDVTW0rwEHiWnloxUVIbohhwvi9ZlJTm83B66sYrMj6XMv6CW8t0FX47BqhdfzAg/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382108637061496738" border="0" /><br /><br />atau dapat ditulis:<br /><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8b8ID6Wj6Aus0JsYdWkOdScUy_U1mOFZP6OA2d5wl2CZTvPDqfk5oARDXfptoDwZ71EYF-ujDUX61uFU8ODk0cqr6zczoayIVTR1If9TnmfF_8eB5a1xUZYzYvJRle54Mcq3vRqoaa4s/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5382108644964490354" border="0" /></div></div><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 7:</span><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAFzrE-q358y37URpD8MoYOIftrH-sPDc4mLmBBEzqe_npso0KmTyrEhEuvZyupHVvC34E-hJ5R6804MyTMQN77mOTukGQlEOTiINU8ZdZ95D0SPI6XfCCW8kZ4CtcdGUHQDxnsEk_Tcc/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5382111693802317170" border="0" /><br /></div>Dari bilangan 1, 2, 3, 4, ... , 121,<br />terdapat 11 bilangan yang memiliki faktor dengan 121, yaitu 11, 22, 33, 44, ... , 121.<br />Jadi, terdapat (121 - 11) = 110 bilangan yang koprima dengan 121.<br /><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 8:</span><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEijPV6ZX_Jihsztd6mZ6mzKmXVcUzckSlOhJvS8-Pqf3yb9CcFfFQpk8XyMlSDvZDbHB5U9yt0SkPflElKMbbbjpYbY-W8VpO-c81x6H4Vbrcrf3b4m-6im1UoXRgr6vz5AeviYuuqTJ3g/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5382113073042415826" border="0" /><br /></div>Dari bilangan 1, 2, 3, 4, ... , 125,<br />terdapat 25 bilangan yang memiliki faktor dengan 125, yaitu 5, 10, 15, 20, ... , 125.<br />Jadi, terdapat (125 - 25) = 100 bilangan yang koprima dengan 125.<br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 100px; margin-right: 100px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><span style="font-weight: bold; color: rgb(0, 102, 0);"><span style="background: rgb(24, 87, 198) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(236, 252, 223);"><span style="font-size:130%;">Teorema 3</span></span></span><br /></div>Phi function adalah fungsi multiplikatif.<br /><br />Untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhluT8Vkql9wllUi7ADWOKaCGk1oEx3NdUZ36YLK19wS4lbYbNfjy1Y4Zc36sNXz06Z9gp7-LYrRE1f-rXY8wkrOwTTKp_KWgfRm0k1raYZK5BXaDgu3LAv2DKI_CU0pqlyDh0g4gYdAAw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382110116619152434" border="0" /> saling relatif prima (koprima), maka<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHRmsASi0p1IlIsdyhjjf87iedEa88_9VLG-8wp8pdAyTl43aPsSQ1fx5wOY2iNutcC_9qm89gUVvuHxn6I4Z4bprEDPeCmHU4tVGXN3PrD_T2xDvcvn8R1-ep2MLrMk36LKfEuAkMIyc/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382110113138596754" border="0" /><br /></div></div><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">ILUSTRASI BUKTI:</span><br />Anggap <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoYYw7uOwi55lE677x0LJy5Da_tN5vsrYqSbZmxipzlsNbTlI3YIFiUvM-YiCXwThmVxx_L-ZpHWesmwJNdsXskx1EQDIdyvwvLZFQ7ckSbmcekQ9ezH6vMdIoq8f9o7n-_thqg3K1aNg/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382228868936736098" border="0" /> dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEij2CD3N9HoCqI7PoNWYefYgaGJP07U7wi8mjNcLLSyWmUDFtSfwg8QaxtnKtL6c0cec7BMXMDlcqrCDUKy6m0qc4XdAFk8CotSn7T-DvoZ18rx-bw-Mz2yjsiOnxM_Vetx_xWEMMV904c/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382228860571174210" border="0" />, maka <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGo9KrbtzjzHMY2ELYB5h_7mPzl6XEtJV0BhzopW1b13_7KYMaWCfgbcclKj7zf1FZLgWO9D6Ky06n40KRl4t7DghJq2tqDGqDHfa7HMIvh6ItAn72pOIWl_rzH9pQYGJdjt5VouRjrVE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382229198474019730" border="0" />. Kita akan mencacah bilangan 1, 2, 3, ... , 36 dalam suatu bagan seperti di bawah:<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfxzuYsJOfxDQO1dvF-s7QNopQYBWCkSHFbbxqonk1ZWNqFK6COo3E0UTKExcSNRrBKkmPYNGIoxBQs9Pgo4R3BWBHGmI-PJGlJv9JeG732T1B_mfakhO9_Qj0x9q3h0Rway78Q2TFArk/s1600-h/chart.jpg"><img style="cursor: pointer; width: 396px; height: 140px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfxzuYsJOfxDQO1dvF-s7QNopQYBWCkSHFbbxqonk1ZWNqFK6COo3E0UTKExcSNRrBKkmPYNGIoxBQs9Pgo4R3BWBHGmI-PJGlJv9JeG732T1B_mfakhO9_Qj0x9q3h0Rway78Q2TFArk/s1600/chart.jpg" alt="" id="BLOGGER_PHOTO_ID_5382233441960767330" border="0" /></a><br /></div><br />Bilangan yang diberi warna biru adalah bilangan yang koprima dengan 36.<br />Dari bagan di atas, kita tahu bahwa <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSr4PoL2c9bZ7HgU1g2vxGqfhezhrgTWBA8hO4MbWKWp3Mr_tEVAVwzHItLaAFkhZJvRbL94C9kS_J0CqiNr5kmfT0c8C8MxYe_poN7FwuzNYuqJdGssbtaOrlrRjBY-IB8-n1pebZLNE/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5382234034099580194" border="0" /><br /><br /><span style="font-weight: bold;">BUKTI:</span><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDV4G6xp_eR9pBWTbRc36pHRco4JVBV_BJssL0xArI2UI1y-NzKUbM3o3Ph1eBKso2GLPiKpc30J4G9JFu5l6ZhixQTF64wGTVSQneN3rjV4En7XTQZ4aaMa_HqGwsl1Ex-5E0w-rudWs/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382235060230143058" border="0" /> dapat digambarkan dalam bentuk seperti di bawah:<br /><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGB9-P8IwMkGOYt5EQrxOUF8e4Qk96oZI6D_HpDwq9QhL8QcKkC0uNwfnzTwV7sFYDoYLLLfTTQJNkN3XJJ7hWzyrFWgVZ5co1WQHXj2ZdFO3oYA2hmiOhwPY8Djtk8vVaaRDaUDA9upw/s1600-h/2.gif"><img style="cursor: pointer; width: 276px; height: 146px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGB9-P8IwMkGOYt5EQrxOUF8e4Qk96oZI6D_HpDwq9QhL8QcKkC0uNwfnzTwV7sFYDoYLLLfTTQJNkN3XJJ7hWzyrFWgVZ5co1WQHXj2ZdFO3oYA2hmiOhwPY8Djtk8vVaaRDaUDA9upw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382236993745130482" border="0" /></a><br /></div><br />(Lihat kolom pertama)<br />Dari barisan 1, 2, 3, ... , <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsAbL_I4gcEq24XCuYGc_Q0vxGMtlQMbJD9g6KA3rg_hZ5JLIDqL7vZBwyrOs3mKw5k6c2UFF9FG7EwxbesrhTOKkJINZSSjj1EmvoTpYz5PkB5OLxeOGzLV4-zQe6F2DgmfiGrQ71r-Q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382240527496362146" border="0" />, ... , <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" />, misalkan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsAbL_I4gcEq24XCuYGc_Q0vxGMtlQMbJD9g6KA3rg_hZ5JLIDqL7vZBwyrOs3mKw5k6c2UFF9FG7EwxbesrhTOKkJINZSSjj1EmvoTpYz5PkB5OLxeOGzLV4-zQe6F2DgmfiGrQ71r-Q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382240527496362146" border="0" /> memiliki faktor dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" />.<br />Kita tulis kembali baris ke-<img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsAbL_I4gcEq24XCuYGc_Q0vxGMtlQMbJD9g6KA3rg_hZ5JLIDqL7vZBwyrOs3mKw5k6c2UFF9FG7EwxbesrhTOKkJINZSSjj1EmvoTpYz5PkB5OLxeOGzLV4-zQe6F2DgmfiGrQ71r-Q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382240527496362146" border="0" />, yaitu:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Re1ZxUpjCjIn4vyQuVO5wCy-BrnFAbdier7axMirOiaigHgQf0hmfVq_d8NlrRvd-BOyjUhXd8f7NhgqyBRFaPVKItXjR8Hohtsjt6vI88at0F0fMbNaxcr48xsQbOZeX3hf1D7Okmg/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5382242629776239298" border="0" /><br /></div>Karena <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsAbL_I4gcEq24XCuYGc_Q0vxGMtlQMbJD9g6KA3rg_hZ5JLIDqL7vZBwyrOs3mKw5k6c2UFF9FG7EwxbesrhTOKkJINZSSjj1EmvoTpYz5PkB5OLxeOGzLV4-zQe6F2DgmfiGrQ71r-Q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382240527496362146" border="0" /> memiliki faktor dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" />, maka semua elemen barisan di atas juga memiliki faktor dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" />. Otomatis, semua elemen tersebut juga memiliki faktor dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDV4G6xp_eR9pBWTbRc36pHRco4JVBV_BJssL0xArI2UI1y-NzKUbM3o3Ph1eBKso2GLPiKpc30J4G9JFu5l6ZhixQTF64wGTVSQneN3rjV4En7XTQZ4aaMa_HqGwsl1Ex-5E0w-rudWs/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382235060230143058" border="0" />.<br /><br />Karena kita ingin memperhitungkan bilangan yang koprima dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDV4G6xp_eR9pBWTbRc36pHRco4JVBV_BJssL0xArI2UI1y-NzKUbM3o3Ph1eBKso2GLPiKpc30J4G9JFu5l6ZhixQTF64wGTVSQneN3rjV4En7XTQZ4aaMa_HqGwsl1Ex-5E0w-rudWs/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382235060230143058" border="0" />, maka kita tinjau <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy-8W9QZ-DpQryDpXOVqzOgYBSE5V_HsIpLB3TRrsgzCsU6d334tLPFWMEPTTnjHBLZuCu0GMOt57DJ766ttU0OSo2Ni6Mwanr0UG78RlXwMV4ZKDeM_58a9cngQuGOD5AoaYodfIoyFc/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5382246371522406946" border="0" />barisan yang koprima dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" />.<br /><br /><div style="text-align: center;">----<br /></div>Anggap <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsAbL_I4gcEq24XCuYGc_Q0vxGMtlQMbJD9g6KA3rg_hZ5JLIDqL7vZBwyrOs3mKw5k6c2UFF9FG7EwxbesrhTOKkJINZSSjj1EmvoTpYz5PkB5OLxeOGzLV4-zQe6F2DgmfiGrQ71r-Q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382240527496362146" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" /> koprima.<br />Kita tulis kembali baris <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsAbL_I4gcEq24XCuYGc_Q0vxGMtlQMbJD9g6KA3rg_hZ5JLIDqL7vZBwyrOs3mKw5k6c2UFF9FG7EwxbesrhTOKkJINZSSjj1EmvoTpYz5PkB5OLxeOGzLV4-zQe6F2DgmfiGrQ71r-Q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382240527496362146" border="0" /> sbb:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Re1ZxUpjCjIn4vyQuVO5wCy-BrnFAbdier7axMirOiaigHgQf0hmfVq_d8NlrRvd-BOyjUhXd8f7NhgqyBRFaPVKItXjR8Hohtsjt6vI88at0F0fMbNaxcr48xsQbOZeX3hf1D7Okmg/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5382242629776239298" border="0" /><br /></div>Karena <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhluT8Vkql9wllUi7ADWOKaCGk1oEx3NdUZ36YLK19wS4lbYbNfjy1Y4Zc36sNXz06Z9gp7-LYrRE1f-rXY8wkrOwTTKp_KWgfRm0k1raYZK5BXaDgu3LAv2DKI_CU0pqlyDh0g4gYdAAw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382110116619152434" border="0" /> koprima, maka semua elemen di baris <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsAbL_I4gcEq24XCuYGc_Q0vxGMtlQMbJD9g6KA3rg_hZ5JLIDqL7vZBwyrOs3mKw5k6c2UFF9FG7EwxbesrhTOKkJINZSSjj1EmvoTpYz5PkB5OLxeOGzLV4-zQe6F2DgmfiGrQ71r-Q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382240527496362146" border="0" /> tersebut merupakan sistem komplit residu modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhluT8Vkql9wllUi7ADWOKaCGk1oEx3NdUZ36YLK19wS4lbYbNfjy1Y4Zc36sNXz06Z9gp7-LYrRE1f-rXY8wkrOwTTKp_KWgfRm0k1raYZK5BXaDgu3LAv2DKI_CU0pqlyDh0g4gYdAAw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382110116619152434" border="0" />. (<span style="font-style: italic;">Lihat teorema di kotak biru di bawah</span>). Oleh karenanya, di baris <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsAbL_I4gcEq24XCuYGc_Q0vxGMtlQMbJD9g6KA3rg_hZ5JLIDqL7vZBwyrOs3mKw5k6c2UFF9FG7EwxbesrhTOKkJINZSSjj1EmvoTpYz5PkB5OLxeOGzLV4-zQe6F2DgmfiGrQ71r-Q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382240527496362146" border="0" /> tersebut pasti terdapat <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimgyKynJ6u86jeEIhgeBFiNFHuiUy_mupIaMiHxcZEqGGCromAi-ALRYSJ5ZH_ToQpwX9NoRLNHjfQtig_7noxoUjFI15oW8buo3QoKfLzjnOe22_em8PD6aaJj8NtKOiypKofXeBnzJ4/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5382250243039512290" border="0" /> bilangan yang koprima dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhluT8Vkql9wllUi7ADWOKaCGk1oEx3NdUZ36YLK19wS4lbYbNfjy1Y4Zc36sNXz06Z9gp7-LYrRE1f-rXY8wkrOwTTKp_KWgfRm0k1raYZK5BXaDgu3LAv2DKI_CU0pqlyDh0g4gYdAAw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382110116619152434" border="0" />.<br /><br /><div style="border-style: dashed; border-width: 1px; padding: 5px; background: rgb(222, 251, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Sistem komplit residu modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" /> adalah kumpulan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" /> integer <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdSwRpWv2LUnVAj5k8tuBAODxvfK4JtPxn_1roFZd5EFLJ0YEPIEn7f4bWaOq3a_s0q2vF36-aHuhSZav5g-MdaeDmXvaDTjYtmxvS3LjHnkiwRwbgKYde7V9_3HRCg-ReBt4mCr7YduA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382586406039968882" border="0" /> yang tiap elemennya akan menghasilkan kelas sisa yang berbeda-beda jika dibagi oleh <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" />.<br />Contoh:<br /><br />1, 2, 3, 4, 5 merupakan sistem komplit residu 5.<br /><br />-1, 3, 7, 10, 16 merupakan sistem komplit residu 5.<br />Perhatikan bahwa:<br /><div style="text-align: left;"> -1<img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXtn1jeZigdu_k55Kratjnck_XNjcMEIVHZq6vw88WD7_ZTw_zZw4V6fIRyyFzV3jXnhZJPUAGl1XqV2hMVjg9UHnAoMMLuEIczypdMtDDwF2E0autVpMAGV4xRnMFkXRn0x-YguHpzTQ/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382589154190163570" border="0" /> 4 mod 5 ,<span style="color: rgb(255, 255, 255);">__</span> 3 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXtn1jeZigdu_k55Kratjnck_XNjcMEIVHZq6vw88WD7_ZTw_zZw4V6fIRyyFzV3jXnhZJPUAGl1XqV2hMVjg9UHnAoMMLuEIczypdMtDDwF2E0autVpMAGV4xRnMFkXRn0x-YguHpzTQ/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382589154190163570" border="0" /> 3 mod 5 ,<span style="color: rgb(255, 255, 255);">__</span> 7<img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXtn1jeZigdu_k55Kratjnck_XNjcMEIVHZq6vw88WD7_ZTw_zZw4V6fIRyyFzV3jXnhZJPUAGl1XqV2hMVjg9UHnAoMMLuEIczypdMtDDwF2E0autVpMAGV4xRnMFkXRn0x-YguHpzTQ/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382589154190163570" border="0" />2 mod 5 ,<span style="color: rgb(255, 255, 255);">__</span> 10<img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXtn1jeZigdu_k55Kratjnck_XNjcMEIVHZq6vw88WD7_ZTw_zZw4V6fIRyyFzV3jXnhZJPUAGl1XqV2hMVjg9UHnAoMMLuEIczypdMtDDwF2E0autVpMAGV4xRnMFkXRn0x-YguHpzTQ/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382589154190163570" border="0" />0 mod 5 ,<span style="color: rgb(255, 255, 255);">__</span> 16<img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXtn1jeZigdu_k55Kratjnck_XNjcMEIVHZq6vw88WD7_ZTw_zZw4V6fIRyyFzV3jXnhZJPUAGl1XqV2hMVjg9UHnAoMMLuEIczypdMtDDwF2E0autVpMAGV4xRnMFkXRn0x-YguHpzTQ/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382589154190163570" border="0" />1 mod 5<br /></div><br />Apakah (-10, 7, 18, 22, 30, 32, 46, 65) merupakan sistem komplit residu 9?<br />Jawab: bukan, karena jumlah elemennya hanya 8.<br /><br />Apakah (-10, 7, 18, 22, 30, 32, 46, 65, 73) merupakan sistem komplit residu 9?<br />Jawab: bukan, karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5nb8-KaH3V_AZTaRkIdjMteWyI4KmBhT3shEWTmfGuYeNW3EDy4FbS2xhs9pwQPT19LRTEGFt2kUipuAt7cF35HFxegXkD29U6Z5Den3iBfN2Zo_GFoFEPk-McgC6vN4mDuXXEgdj3Yg/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5382593302814706290" border="0" /> dan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwTKallIeFH2NnB5IGwkTxmq4cdpvjeuJoux7hurAHsi0dRoPc3w8lSP9w92fnCQ1Q75nMFf9JIdFMxKXFxlhREP2OvanAxGgMUuSVN3gWdJ116Ch13QVeUAkDf_5zgnUMceaoB3utbAQ/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5382593296391389170" border="0" />. (kelas sisanya sama)<br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(222, 251, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 20px; margin-right: 20px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><span style="font-weight: bold; color: rgb(0, 102, 0);"><span style="background: rgb(24, 87, 198) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(236, 252, 223);"><span style="font-size:130%;">Teorema</span></span></span><br /></div>Jika <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdSwRpWv2LUnVAj5k8tuBAODxvfK4JtPxn_1roFZd5EFLJ0YEPIEn7f4bWaOq3a_s0q2vF36-aHuhSZav5g-MdaeDmXvaDTjYtmxvS3LjHnkiwRwbgKYde7V9_3HRCg-ReBt4mCr7YduA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382586406039968882" border="0" /> adalah sistem komplit residu modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" /><br />dan jika <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEig8zA3KSiiuF61Ql_Fo1IBaBqDiYzfsdbrEaZoUwP5GI5AZUA3aP5Fb7vofI-HWvSe4D-lEQKfVs_Q3hpt2qkq5eOlPUF9dK_-B3ae2qf8qJMp1YP6k_w0C-gY790S6NWdJPHRI8wZReU/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5382596284941816162" border="0" /> adalah positif integer dimana <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmu2l9rAr-nNxGJoFROfjvqfssL9j2lzmtl6-nD3RNX0fjT8CWqYrlEOeZGb0e8gDAI6iEreWhF8pAo8UBVQKEQzWeuph0VRSoJ7WB-ntOYcitd9Ng1TQr8wl4kCSTwUzF4D8TiMOyYy8/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5382596274282395170" border="0" />,<br />dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpT_sEe3hpxD6xwwXujEcIZ6uIfRMqM2aXAKVdOxh7f4qZCeLlUWpgfKa3in4lWUo_sutVAHt2CG8jZPh0BUEkqjuUM1MAjrULA-FgqgQX3Mv-F50hlHh7MFlacRen6E9GtbAJae80lRk/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5382596656917493778" border="0" /> adalah integer, maka:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJMn_JEdhk1OWPpRvtlrqhAUHqFOTMXMDlSyoTb-xd6DuiuQEmx2GS46eP0BxiBixc74FXno8PbqZSu3MYewGf6GpnGTE2JVQj4TiWdOqRyLYJmui5ASzDtG9N9Bgpsoa8xd3lsSEN_Eo/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5382597107310367474" border="0" /> juga merupakan sistem komplit residu modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" /><br /></div><br /><span style="font-weight: bold;">BUKTI:</span><br />Asumsikan bahwa ada dua elemen yang kongruen, maka:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRg-T72qPoimbn7pLovncfiPCWJhObZi9wQ3aFJovbcLcLwyA5kSeQ_JsiHXVCkKVvDT-SVmNKmVsienwc5t57KKVjBLn8wdWqxpimV_0wvGnp9yBuWwuwTL45kk8jgjldWVsqOE-Deg0/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5382598179991816578" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic1zRvlJidkK5KYeGOR-OdlJSwJGhHXCQAzcmbc-d90up2iA7MiQXEnxQ4p-7_NwMEruQLW4J30me98Nznv6PvPCqjWjmrjI7AaADod4utvWRYsHxKfXpj1ld2Oe8goKQCMhhyphenhyphenXaefVy0/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5382598171514016802" border="0" /><br /><div style="text-align: left;">(<span style="font-style: italic;">Lihat </span><a style="font-style: italic;" href="http://hendrydext.blogspot.com/2008/08/modulo.html">SINI</a>) Karena <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmu2l9rAr-nNxGJoFROfjvqfssL9j2lzmtl6-nD3RNX0fjT8CWqYrlEOeZGb0e8gDAI6iEreWhF8pAo8UBVQKEQzWeuph0VRSoJ7WB-ntOYcitd9Ng1TQr8wl4kCSTwUzF4D8TiMOyYy8/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5382596274282395170" border="0" />, maka:<br /></div><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ5AkyhjPjxM94N5cPb1yySVWZfUrnriUPE48eNqClD_x1CDX8y3iUOYIG617SXNBZd8X2mTNoAjipMrthsoFb246pgzuPZE1fAq4FZnui9Zl4PmD3qTs5Fb7l_T5_0fsLu1dcTIyIAG0/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5382598167104814402" border="0" /><br /></div>Namun, karena kita tahu bahwa <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdSwRpWv2LUnVAj5k8tuBAODxvfK4JtPxn_1roFZd5EFLJ0YEPIEn7f4bWaOq3a_s0q2vF36-aHuhSZav5g-MdaeDmXvaDTjYtmxvS3LjHnkiwRwbgKYde7V9_3HRCg-ReBt4mCr7YduA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382586406039968882" border="0" /> adalah sistem komplit modulo, maka tidak mungkin ada kelas sisa yang sama antar <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrggcpk_Zv7f7W3Sr3s1rQF6l9uusqbZnnbTa5XbcaVNjf8djACbX4xiaCyoeFU_HWrSiY3SAYX55OsCCMIch3PEOWDRZ7UO5Ph2Istwihi2fqWj0wjbbvTLV2t3U7TNmuF27CO1ImZMA/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5382599363290923554" border="0" /> dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCeED3YciRpiCD1rEWZBKP62QTXQ2KrRcrjYjw7b23xnDWhaWqqvHXQhtDVXxv_lYKlOIB-gz5sN0_1KIjAIkC4JMkWBEbytEZt4nY_IbiQCxtXEhHKUBG9Oqf0ezFbmYbi_UpJZd5-ZE/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5382599362026424498" border="0" />.<br /><br />Kontradiksi dengan asumsi awal, maka tidak ada dua elemen yang kongruen modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" />. Dengan demikian, <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJMn_JEdhk1OWPpRvtlrqhAUHqFOTMXMDlSyoTb-xd6DuiuQEmx2GS46eP0BxiBixc74FXno8PbqZSu3MYewGf6GpnGTE2JVQj4TiWdOqRyLYJmui5ASzDtG9N9Bgpsoa8xd3lsSEN_Eo/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5382597107310367474" border="0" /> merupakan sistem komplit modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" />. ■<br /></div></div><br />Karena terdapat <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgy-8W9QZ-DpQryDpXOVqzOgYBSE5V_HsIpLB3TRrsgzCsU6d334tLPFWMEPTTnjHBLZuCu0GMOt57DJ766ttU0OSo2Ni6Mwanr0UG78RlXwMV4ZKDeM_58a9cngQuGOD5AoaYodfIoyFc/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5382246371522406946" border="0" /> baris yang koprima terhadap <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8hsDVu8wtxdRcvVcNChKgQE6XvDd5lO4LZgcySr8ptWmYY5x65xiToysSZKZbGqbFD7twXRV49beG2fCWpYNn5IzWrYJe9se3fGon4gi2nWJxMBhnRpq5Kp780A0cOcDbuWy7Ya5oFPA/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5382110122556300258" border="0" /> DAN di setiap baris tersebut terdapat <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimgyKynJ6u86jeEIhgeBFiNFHuiUy_mupIaMiHxcZEqGGCromAi-ALRYSJ5ZH_ToQpwX9NoRLNHjfQtig_7noxoUjFI15oW8buo3QoKfLzjnOe22_em8PD6aaJj8NtKOiypKofXeBnzJ4/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5382250243039512290" border="0" /> elemen yang koprima dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhluT8Vkql9wllUi7ADWOKaCGk1oEx3NdUZ36YLK19wS4lbYbNfjy1Y4Zc36sNXz06Z9gp7-LYrRE1f-rXY8wkrOwTTKp_KWgfRm0k1raYZK5BXaDgu3LAv2DKI_CU0pqlyDh0g4gYdAAw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382110116619152434" border="0" />, maka dapat disimpulkan bahwa:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHRmsASi0p1IlIsdyhjjf87iedEa88_9VLG-8wp8pdAyTl43aPsSQ1fx5wOY2iNutcC_9qm89gUVvuHxn6I4Z4bprEDPeCmHU4tVGXN3PrD_T2xDvcvn8R1-ep2MLrMk36LKfEuAkMIyc/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5382110113138596754" border="0" /><br />TERBUKTI ■<br /></div></div><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 9:</span><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiOxmVaj2TsBxS_xshL_0d0JN6eFvQodp59Zpn0qJyfDKba0tXgNbxps4ejjv36lL4v_k4seLhNXu8EiShIYStfFlw_99Ukp9uJN2ohoHYrOWg4mCbCLWfYYyM7RxvZK9yMEVhcMC5zNw/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5382252897914126930" border="0" /><br /><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 10:</span><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_n2ZnbDTkjxIk0j2Pri1TkdWGuw3PU0UcJWfi1-IkiOyWsfQiWwPI7EDYrmJNKsncu85cumky3L-0FV2_KmIl3O1ScFlJO-yRYxtDZFT6INNVj0uC_a726gijBtW2x4yVjhnmYJwCbaw/s800/8.gif" alt="" id="BLOGGER_PHOTO_ID_5382253642232552338" border="0" /><br /><br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 30px; margin-right: 30px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><span style="font-weight: bold; color: rgb(0, 102, 0);"><span style="background: rgb(24, 87, 198) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(236, 252, 223);"><span style="font-size:130%;">Rumus Cepat</span></span></span><br /></div><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhG5SJfiEm3JHnvPv3m5bo96RXdrvGYyaROAH7YfmAVOHJiENvjYE_zh7Kgj8tFJo2rLGGgYsSwoCwWb5aEjdaLHVrf9DM9edqSVgstmaK80lmkTqFFIsxAKTV3w1gbvq4kuXMb4fMCPMg/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5382255910719019042" border="0" /> merupakan faktorisasi prima untuk positif integer <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhluT8Vkql9wllUi7ADWOKaCGk1oEx3NdUZ36YLK19wS4lbYbNfjy1Y4Zc36sNXz06Z9gp7-LYrRE1f-rXY8wkrOwTTKp_KWgfRm0k1raYZK5BXaDgu3LAv2DKI_CU0pqlyDh0g4gYdAAw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5382110116619152434" border="0" /><br /></div><div style="text-align: center;">maka<br /></div><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPzDDqL2r8Fgkk9fFQTUF2UkFe42uI8I75pzNOlFJGuS4G0dDLtt9YswhmEdbgePKv1VLW87hnxcclCyn6M-6QA4nWytGFj9aE1BFwtnxrbzIPvCcPnHyzg87DF2rPPD2RAVgiMb85pnU/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5382255232232380338" border="0" /></div></div><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">BUKTI:</span><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW0t9uqmjXDSSF72_XCsz-tvRjJvrx26AEpSYBn1fe1BI5sx336w-D8uL0qKLzGbFqP8twReLZyfRppE3mVLaYaU08QY2McdzkXX34DT6D7esRWCCDlnnpZ9fiPLGiniWVXEiB0a-8nXk/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5382255915645488386" border="0" /><br /></div><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUvp7kSwbGVVucq5O8bloJitzgChDNbvr6SLN-BNcCExlP9X-ySnI10zofrKpUGNqiOj5Ekw4r5XU_d-WNvi2HmDQ6-kuMHTm9zYLpD7l-kSglFqQPLnQUscM4Xy7oxVVHzY8xYF-OaAs/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5382256894710318450" border="0" /><br /><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyHonJ-eRshltLa-_GEHVnQWdDZaHw1Mqg1EPIyIjD4fT2B_HfCvbCQoHcFF5i2GeFnuk2c3czb4iqWU7BgGEoOcDxVQLKYCO5GJ93V3JPmzSJmjjkPSDxQK9q-V3dm86AhtUVCN3hxS4/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5382256888724428706" border="0" /><br /></div><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPzDDqL2r8Fgkk9fFQTUF2UkFe42uI8I75pzNOlFJGuS4G0dDLtt9YswhmEdbgePKv1VLW87hnxcclCyn6M-6QA4nWytGFj9aE1BFwtnxrbzIPvCcPnHyzg87DF2rPPD2RAVgiMb85pnU/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5382255232232380338" border="0" /></div><div style="text-align: center;">TERBUKTI ■<br /></div></div><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 11:</span><br /><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhG2BURvEP3Q3ySkLV2St6DKStHLgE9mnhNxzB89r4UgI-whW5UtcVE4BCDjK0ZIf-R8pAqI1NjWsq764UDUp-_ChZlpZ-xFNFMngtlM_1oV7X55Dmfja_EBpdjsxaa4ffTcxUh8KNKfWc/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5382258427276828018" border="0" /><br /><br /><span style="background: rgb(100, 200, 200) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 12:</span><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirf-D0tAPrR3lOccRMeubB9hdv4JaFL-vQ_vkNLPEGF-o-7dcGH8RnLGEGJaKuQz8jyl7UdYGZ1WDhZc5akw9intQqX4AZRMckPd18-Ng4NF6CjNFdDWIdiAXdhebWAiK06SE4CxjqJ_0/s800/17.gif" alt="" id="BLOGGER_PHOTO_ID_5382259710105483314" border="0" /><br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 30px; margin-right: 30px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><span style="font-weight: bold; color: rgb(0, 102, 0);"><span style="background: rgb(24, 87, 198) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(236, 252, 223);"><span style="font-size:130%;">Teorema 4</span></span></span><br /></div><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8l5U_AHfW2nUDCGj23g7-d0UJhyphenhyphenY-9US3vi54wLMpsLtziHUI4hzIzoXBhFBNh0t_3pqvQRB0G17t5-yYKf38c4ZcTXQ442F0isCVQg_FH9WAYHJ81Sqx-Ak_vHbxRaYeQ5eOEK5-Jv8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5381663184909137362" border="0" /> selalu bernilai genap untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc9P_NqL9DbXVHzUiMAXpZU9r07rSvc11zK6nhoAfquI10BuKep3V1yNGrOCcltuoVIkPA9PhD4Ten_7GWgwNmRjBhQ5QkRYsQER2QjIn83QTajKkSXeMvNKQYLcRaqDX7NvV_bAKzQ74/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5382261816488146706" border="0" /><br /></div></div><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">BUKTI:</span><br />Anggap <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhG5SJfiEm3JHnvPv3m5bo96RXdrvGYyaROAH7YfmAVOHJiENvjYE_zh7Kgj8tFJo2rLGGgYsSwoCwWb5aEjdaLHVrf9DM9edqSVgstmaK80lmkTqFFIsxAKTV3w1gbvq4kuXMb4fMCPMg/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5382255910719019042" border="0" />. (faktorisasi prima), maka<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjW0t9uqmjXDSSF72_XCsz-tvRjJvrx26AEpSYBn1fe1BI5sx336w-D8uL0qKLzGbFqP8twReLZyfRppE3mVLaYaU08QY2McdzkXX34DT6D7esRWCCDlnnpZ9fiPLGiniWVXEiB0a-8nXk/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5382255915645488386" border="0" /><br /></div>Dari teorema 2, kita tahu bahwa <img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi04NzSP1iuTnzGWzMBKjxfGUknmjTsJyTMUuzRPo_n1MIhfCx5fKB36IQ9izo9YixnC-siRwGDr8zss35_K8EZmm-PF7sP7N5cNY5wRUBETICJA05qhn9OmDiYcjbSnjS1VcfGt-FwJxs/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5382264190329899650" border="0" />.<br />Perhatikan bahwa <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTj6JRYutHidmK6GADusz1ft4f4F5a23puXVTYrfC5092SvoweeLt9d-k519tnHhbiT8b4baSVabEOudYXYIV0Cy_1Idfn-t5zLnezKaG6TjYGpZpH9n_xRWrXDhjmoWNrc_8ONn-K4Lw/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5382265687778796834" border="0" /> selalu genap untuk setiap <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjufB0Zv4Y1-MSISGDw6t9pfjJcoAFK6eqsm1tpS9lsSsb_HIH7UZkGqBIm45-6VxpHjZQGAIu_qfo8DTaIwDbK6uj67t-xEdnYgkRNM2lIn2Ax1gnXiLVwiMFv82bQsx3Qp5UxeXqMMvo/s400/24.gif" alt="" id="BLOGGER_PHOTO_ID_5382266158207352594" border="0" />, kecuali untuk <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAE6RYRlJuSFthzCM4ZXaVjcNzqgm3zWb7YF2b9zKvO28XmNJTE9IMYoDdYn9xS5csemskNduvqHDgBX1C-ENfdJC-lSuZHJogRUq_o6PHzgwLDOcdHoTsWFUttK5baTxrd0rAHQuP5uo/s400/25.gif" alt="" id="BLOGGER_PHOTO_ID_5382266147942051986" border="0" /> DAN <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1SjGeZfESOXanVHaylqjOJMxYKm6hZzF_APGQgCmEZ_qKPMOTvJlQpcEFWUbJocQR15wZFwKP2h8r3P5sVda5knoHt-4umFKW_vs7Guy0r3oGwlziIdUH4C2ePBFwJelkGHtRznpAgE4/s400/26.gif" alt="" id="BLOGGER_PHOTO_ID_5382266144216048290" border="0" />.<br />Terdapat satu saja <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTj6JRYutHidmK6GADusz1ft4f4F5a23puXVTYrfC5092SvoweeLt9d-k519tnHhbiT8b4baSVabEOudYXYIV0Cy_1Idfn-t5zLnezKaG6TjYGpZpH9n_xRWrXDhjmoWNrc_8ONn-K4Lw/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5382265687778796834" border="0" /> yang bernilai genap mengakibatkan <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8l5U_AHfW2nUDCGj23g7-d0UJhyphenhyphenY-9US3vi54wLMpsLtziHUI4hzIzoXBhFBNh0t_3pqvQRB0G17t5-yYKf38c4ZcTXQ442F0isCVQg_FH9WAYHJ81Sqx-Ak_vHbxRaYeQ5eOEK5-Jv8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5381663184909137362" border="0" /> juga bernilai genap.<div style="text-align: center;">TERBUKTI ■<br /></div></div><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjad3DbDTlTVZLtUMxHUx01WBrOIujb4om9ZAkZJBlts7XAlgLQLD_s3tDXchtUL_1Pb3Spd8BqRD9azOtYW_BwzAMa37Jg-JUCS-jVhxig4Mr1GvxLgSIH48bVHKIBLZFmGQOl40DUPX0/s1600-h/closing.jpg"><img style="cursor: pointer; width: 117px; height: 26px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjad3DbDTlTVZLtUMxHUx01WBrOIujb4om9ZAkZJBlts7XAlgLQLD_s3tDXchtUL_1Pb3Spd8BqRD9azOtYW_BwzAMa37Jg-JUCS-jVhxig4Mr1GvxLgSIH48bVHKIBLZFmGQOl40DUPX0/s400/closing.jpg" alt="" id="BLOGGER_PHOTO_ID_5381682204857114162" border="0" /></a><br /></div><br /><div style="text-align: justify;">Selain bisa ditulis sebagai <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8l5U_AHfW2nUDCGj23g7-d0UJhyphenhyphenY-9US3vi54wLMpsLtziHUI4hzIzoXBhFBNh0t_3pqvQRB0G17t5-yYKf38c4ZcTXQ442F0isCVQg_FH9WAYHJ81Sqx-Ak_vHbxRaYeQ5eOEK5-Jv8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5381663184909137362" border="0" />, phi function juga bisa ditulis dalam bentuk <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm18f9qRrTgzMz0jbVPF89HT53otxikhjmwP8hyrpq_serZ1bcBSLqzNWch7N_vsK49AhBYHRfbe-G3PYzaFOTrr5cIZ_aQXdpmWLL2wMf4MYHGMVrivqSB6WIf7O52cpypHHi1n9T2qo/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5381693683150993378" border="0" />. Ini hanya merupakan masalah bentuk simbol phi saja. Ada yang curly, ada yang straight.<br /><br />Phi function memiliki banyak kegunaan, terutama di bidang kriptografi (persandian). Namun, karena keterbatasan tempat dan waktu, kita tidak membahasnya sekarang. Di post ini, kita hanya belajar mengenai perhitungan phi function saja.<br /><br />Lihat lanjutan post ini: <a href="http://hendrydext.blogspot.com/2009/09/teorema-euler.html">Teorema Euler</a><br /></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber:<br /><a href="http://en.wikipedia.org/wiki/Euler%27s_totient_function">http://en.wikipedia.org/wiki/Euler%27s_totient_function</a><br /><a href="http://mathworld.wolfram.com/TotientFunction.html">http://mathworld.wolfram.com/TotientFunction.html</a><br />Buku Elementary Number Theory oleh Kenneth H Rosen.<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com2tag:blogger.com,1999:blog-8125318493233557109.post-32878032600032174122009-09-09T20:39:00.063+07:002009-09-20T11:47:00.333+07:00Fermat's Little Theorem<div style="text-align: justify;">Dalam teori bilangan, Fermat menyumbang penemuan yang penting, termasuk Fermat's Little Theorem.<br /></div><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 30px; margin-right: 30px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;">Fermat's Little Theorem<br /></div><div style="text-align: center;">Jika <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" /> adalah bilangan prima dan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsLikLpa-_rsbOShQ-FoFhnVQL94awKhj7_9ddOn9A4Vgp9rOlHb53ROyBOw-GS7YAC_GFEvoWKRIsjAfAhSWP4q0y7105fmvaBOEY3_hnW45O5kTAy5G7gxjidr-nS5oKIeEm7vl36II/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380389911748218162" border="0" /> adalah integer positif dimana <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNXRJRHISzhYQ_Vae880EQq2xa3tRAs7y0Gdr59bNPPxjd9z7NL2gpupAnaawumWhv31-LBTxdku9ahD7sIzw4PiQrgzLpX9PVqxB5o4JRxT0-MA-fgcQfiy8XbzwBbItOKE8N9VXZC4w/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380390364084163426" border="0" /> ,maka <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5zMtSrBLQesP0fblXMpd9OEtSN90LhdNm8aDoJUz1mwPobxdGkoZXqQNxKYlXhzRj2j3zyX3h9q-p-F4zXJzwpOyEYDCqJS0Eu1BI1y_Q55xg28H3vKarzto5fyeumyJa2J-5XwcI-jg/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380389898829856338" border="0" /></div></div><div style="text-align: justify;">Fermat menyertakan pernyataan ini dalam sebuah surat kepada seorang koresponden matematika, Frenicle de Bessy, tahun 1640. Dia tidak menyertakan buktinya karena menurutnya buktinya terlalu panjang. Akhirnya setelah berpuluh-puluh tahun kemudian, bukti teorema ini masih menjadi misteri. Tahun 1736, Leonhard Euler berhasil membuktikan dan mempubliksikan bukti teorema ini.<br /></div><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVAFzBjQUSGQxRRzHX6lm_H9Z-s4XOcpxlQDaqX7aNyklF8rDSy8lw51T7_z33IRh3TY6QBwYCFIzqmH2K_LTGknXnOlJh1f7YdwLMF22d48aX6kpSY8VYxq6pJTSjUxaRZWTU1kkTYoY/s1600-h/judul1.jpg"><img style="cursor: pointer; width: 318px; height: 25px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVAFzBjQUSGQxRRzHX6lm_H9Z-s4XOcpxlQDaqX7aNyklF8rDSy8lw51T7_z33IRh3TY6QBwYCFIzqmH2K_LTGknXnOlJh1f7YdwLMF22d48aX6kpSY8VYxq6pJTSjUxaRZWTU1kkTYoY/s400/judul1.jpg" alt="" id="BLOGGER_PHOTO_ID_5380393443812299554" border="0" /></a><br /></div><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Untuk menjelaskan ide di balik bukti ini, sebaiknya kita gunakan contoh sederhana.<br /><br /><span style="font-weight: bold;"><span style="background: rgb(235, 151, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 1:</span></span><br />Asumsikan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0sJ49zFVT298qUGftDo0UETDOQQ5egGTfVCVIF4RUzfRx4koW6IVhhYicolxziKn36HahBGxJdPzyqgj_h508LD1UBe_-kib0voh71wK6YoDOhQjnQ3wK7brd6hm7oHH8rovqb4WUoYI/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380397613553415266" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkdoJmNJeFToN-Skb_mvhPOSXpOnzN9EX9AAhMpGp0ZtDKx6cg2fsuKPlzfnQfPGXxU3IoOGAZb8fuFGIX9DqzZevy9AcFGOdjzbA9gjIDfWpeS5XsuQwHanZ9tw2VBSG9XLBd3mhfXAM/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380397605876737538" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJgVRtxRKCKYc6M_fvkHHSMP6n7tWdVWvRcX0y-jRr30LypC3wPzGleidX6BdAIrovaB0JGxotBv74Akw5m7S0EnojRY45EvWgh2HD1UM94oAg_9-fyLmchKu-dPjxKGcS2tRHvvh_jv0/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380398640214779554" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiy8r2x_nNOcOE5OcLwJQ8Z8xE27NoEw2VIazb5iF6PCC018hIO1aBNrGhFuQYGzNh1Op6D_FnE7wZ9qmDHuyEHkckbSUmic8UIEjygIOCdJs3fVj7r0AiINCJPR_H7j2xlZik-2En8FBs/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380398559367540082" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXw1moRMv99fXCmJskGnibZ8qg2Epx7o61f4vVW45LM6ZODyKoHZJVgOZSAuzDljgmJFdS2-iPi2a8I6zDFWPBfj2HHX6_5Dkuy9T1D_fI9dIfn0nOzivsLmsnPLU6vgbul7UXbCJzsI8/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380398555540023394" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtvyFiOhqtlC7SRi39h5iLvkiaKDIbZa3ghviV8ZaZsga-Tw76CJ1crL4D-wFLGYveQ7GBXI3sFoGInm3CXLQszyj9MeDJAvJrGqAjk8fryaUVkp0pqufrnTKP3xkYeTrgD1r1J5Y_cR0/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5380398545664344018" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRvSfA5UlfKok2AhBcBQTMB6z0lmf5OUgtkUrgTPKDdcgPUKJJU0bRgN3BoZabY1ZSRMbxRzKtqj0bXtyw4rb2qztUuruQ5YIvH8Shx2yCrCCFd-FvX8xURXhWySzIRE54Ai9SXuuuee8/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5380398539351918162" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrdQDTGE1BWYnbUUaR1DjJo3JMfn7Vo3M4zNoP_p7vQ0bUjCpBYQCvGkeDJ-T1og3yBaRJvIjq_uhBPDH5vCPvQz8IKqIaBJJY-CD9LdHNjVgg5kHs-Yum67ZAuSFBSzfNsgYEKaJq27A/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5380398534561358306" border="0" /><br /></div>Dengan demikian:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXhJXsCubDw6os9Zo88TzIKZRO1bsvbAEQ_rY_RVdhnCUTI4ky5FCTy9wDNMCsdM9ih4rcwVwi1pLBZO2nOdbcj8uD3B3NWUAqdjw4uhVTAi73YLc_VXiqmOnygM2qNupf6NjcaoAkXMA/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5380399950515712850" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoEwRruFuvG6CZWkRrsodhZ2K8ynOZeZY9uHgB9BJd26Fmu1EzeoSjbrYe59zptDW1hdZjGLFkYB0oycjePh1Z3QOGmpC5aDdlT3UhPrBsVMdnegq_bDbr27e9EXm-OhEZXTl7PGRJtW8/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5380399943863154018" border="0" /><br /><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz7PuCbmktGSVPkL7sMl_xLeiWtRkb2rptl0-R4LCd63Mb-a0JlzjBsbu5ReAKVbAH8NceEkeUGNE1jdcwwgyZA7-EOolGQ39I2ZALX6hGJZoD_iEaMEH0Glj0RK_VcxDETI4qDuS44bU/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5380399938927719042" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3yfM9qJOgZSgT4aiAE-iKdhdbmFkNsENW1KOHfh85G2hKkYVQekSMZM3t9JTI8wprXqiAHPUFqdgeWNB5D00jOMXbF3PUJST_UeG5HO02SWuS0z2IdDgj7h5Pzp6I2bzXSImkHAqwZTQ/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5380399931028448882" border="0" /><br /></div><br />Note: <a href="http://hendrydext.blogspot.com/2008/08/modulo.html">Lihat hukum pembagian modulo di kedua ruas.</a><br /><br /><span style="font-weight: bold;"><span style="background: rgb(235, 151, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh 2:</span></span><br />Asumsikan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU4xsWe_DtspIts_C9QSCITneUPpo-WMa3gK-oVcQXQJENMWDqOCBpcKM2yyw75zP00tJH1O6u-D6eIz6YESG3bDJ_s7F4X5W_EQ4jB7PKH4JMQ8J6njFwOu7fWNTtjx45JZJtTh7xhEY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380401227643001282" border="0" /> dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKYCe2wOj0eHsLNuQyREEfD3Azl9FkMgIpO36ALgh7-manAX2X3tgxlOTmxYRqq5lkljK2bJ-TVGlQtcgJjKZSM2Kr2WWsoc3Wx-ptI9iM4F5soKoLN10zDMucvpwhimOAURcb_6RZdGE/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380401216718973026" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjV_zEXfF7m7mxjCXV49PT-lp5iaz1GbxJ-w25qohGTdZPKSB7V120B0Kiu7QLX8CL5rOe4jObqLM9Od4Ugzzc-ySgxIdtTPoRnNTcx83FbfkHNq1C1gTfapb2Oi-C8kOTqePPRDWVnwWg/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380401827935152770" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKgDmqf-nJ5JDwNSDQ972OupWQ6rRLI-dpY16VOdZlbY16e988FwIYijA-iRTerxrpz2oOHcreGI8zuDdxvFvoUBW5WwppR5ktUrLjQTCcnS4-EprdPgg9qXb0SlFo-CsjndKh9v6ou0I/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380401819373592914" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhson97DUtjnhBX7O28M-OR7GsN8Kjx2UFhvsO-PAkMnbsZsTYMPuWidCtclLQ1TJZ1Fap_pt8WeGLLSmJ9P1F7uLbkTNw6OEgJcgDD06bIgCut-nEBpJX5G8wl4f8MzAF4L4Jif_KAI4s/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380401814580817570" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdeiY38lBk33lYD8v-ScTY7tI_ns5Hf-62QWyGO1jGiWsA5vYb9kUqd5fBH9jAAugjDNxm3_MFSovXfz4afjNO6jjcPQW_65sLIXA-Rye-ruPI0b81RGNcf6kJm3kBdEhZKQmJ8kz579k/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5380401811252370226" border="0" /><br /></div>Dengan demikian:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6JfAw_t0V3IA4K9v4DLS1rP9Gx8QZhX2nediB4eKcajJXEbjPDTarwhsefbecDqW8gKB0rNHjSWs070XSRp0J_3vmkVoZCFUWD_5wHwrMaCMGLmdf4T0Ais1OUskE6IMx0FAKgfZAFns/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5380402763676849378" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhou8Lij7oC-FdY1DNSUa_RAOmbXanKmXh0_2hfcDPfbjNWutPV-8OK8eaJJF7Cn8pWMvTQfL4SO5iIzT61arYqQxL26Lb_Q336I25JMCxCskaz-OceK-aNv77xlrgz6Y4C3dXAuATNuak/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5380402753027581970" border="0" /><br /><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI6KCzeInlDuLjxqR7pnhUrY6gBW4iFc4NdVGiOaCRRgOv-pglD11nap4aoiOktQqEWICtoA6aWVGEtOXuzsmwfn592xz2ddUjIOPv2U5V7t5syruOOplRvQjP0KIR3h6JmQm67uWsO2I/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5380402747613055362" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjn5w8tY7wcRIHSidnCsxVNzmw22Y3BOrxTHRv7cSrn0CHlJCxDE9rpbo4NaxXgSyfR7KWbvIdccLOUG9jUzTwGdy-iZ2hgKM1zUKg8qJObaUqGtG-fZensDTnsPsKyKh86rr4WBy-E60E/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5380402736082141250" border="0" /><br /></div><br /></div>Dari contoh di atas, seharusnya kita sudah punya gambaran bagaimana membuktikan teorema ini.<br /><br />Asumsikan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" /> adalah bilangan prima.<br />Asumsikan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsLikLpa-_rsbOShQ-FoFhnVQL94awKhj7_9ddOn9A4Vgp9rOlHb53ROyBOw-GS7YAC_GFEvoWKRIsjAfAhSWP4q0y7105fmvaBOEY3_hnW45O5kTAy5G7gxjidr-nS5oKIeEm7vl36II/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380389911748218162" border="0" /> adalah integer positif dimana <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNXRJRHISzhYQ_Vae880EQq2xa3tRAs7y0Gdr59bNPPxjd9z7NL2gpupAnaawumWhv31-LBTxdku9ahD7sIzw4PiQrgzLpX9PVqxB5o4JRxT0-MA-fgcQfiy8XbzwBbItOKE8N9VXZC4w/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380390364084163426" border="0" /><br />Asumsikan terdapat barisan berikut:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_jz0iZEVHl3s53PyTpwSzT3AxGt3CG3DdoeA00zZzXCACITWeZbOXrhb77K277vhrBKU5TS-zk6va6fxXIBHNIUB_wPAFqnh4hOj9O8gkZJobzA3C8YJYKt2pRvGOTNXHy3chYxQATRY/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5380403816801856610" border="0" /><br /></div><br /><table border="1" cellpadding="10" cellspacing="5"><tbody><tr><td>Perhatikan bahwa tak ada satu pun suatu bilangan dari barisan di atas yang habis dibagi <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" />. Alasannya sederhana. Barisan tersebut terbentuk dengan pola <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOai8rcc6vWBbg_HU1n0h1HnvFc4u9amovMoExbpHVdVeIvTnA-510u7ptHk3ekRkXfMPbdoC_58ouYrnIr2QrQ9tUAuXsP7xjj9zn2disSuMmOnzBbHde5msxaSWPg9ykufbzGhP6qiQ/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5380405359042727058" border="0" /> dimana <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmLB0V-NOXfeDf5fYF6OTHlpFS2uT5JFGFENR40CKmjMU-Ay44ON-KJ4B4XBxIPmZ_TDgwX-1BoyMpn1ItjYqaI04Qo36HsaB6_TERwzSeTYzRw4VANtOoN8aFKGvAW7C8u6ce2ozynBM/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5380405350085926946" border="0" />. Oleh karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNXRJRHISzhYQ_Vae880EQq2xa3tRAs7y0Gdr59bNPPxjd9z7NL2gpupAnaawumWhv31-LBTxdku9ahD7sIzw4PiQrgzLpX9PVqxB5o4JRxT0-MA-fgcQfiy8XbzwBbItOKE8N9VXZC4w/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380390364084163426" border="0" /> dan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2uzz6tNR4YSlK2ZhT7c_fFCjBs9sWx5-kqxMf6620-HKLtGuyfw5IWr3EdDYF4x_A6giAVRnpPvxyekKhBt13PI7pCYYDu2yDg5i_KRmikxoj8CQ23OtbsdDM439vWNTp4n0QbD71Ueg/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5380405772314047890" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKgBTNvmdTeTRbl6c3XuZbeYzl9LjyOpf4BNP89yudTEZLG8pDYysliPSlfRftFk4f06o_MbBriQohpCuK72D3nCC4PAfC9r-G0WzeE9JMseScg8DKUygkwBuUctrg3Hnp1znDr8M-2wo/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5380405768506627282" border="0" />.<br /><br /></td></tr><tr><td>Kemudian, dari barisan itu tidak ada dua bilangan yang kongruen modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" />. Atau dengan kata lain, jika bilangan-bilangan tersebut dibagi dengan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" />, maka sisa pembagiannya akan selalu berbeda satu sama lain. Pembuktiannya juga sederhana.<br /><br />Asumsikan bahwa ada dua bilangan yang kongruen modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" />, yaitu <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvp61FjHAuylG1Ub_WFwu03wswHWUSaXzFT751Cg_1SJPmU4jnpVlDD51fkeJLM-OlNi5BqxVmVRyFgTJ4hyphenhyphen1HHsNQF5PA4JZwfyTa_yEAyGfFfRpVrpGo0TIWjkuWZuG6yTFolhmsM0g/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5380407689101115762" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVZ7yXPiW3jffFCPELnnA1IsVPLT9GfM1crcX1mjQ_peZlgd1r1sRgAzdMNdh2SFLf0ELjYlwQaSR_sGnpPl45AFmw2DaPP3QjSP-7LqmL5g5kBX2mYJ_UXFT4iCeh2Kf5bW208Xrr0dA/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5380407681789161858" border="0" /> dimana<img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhP6Ka2Xrv5SBdp3C28EkUrfWwv-EzEIxfzblOy-Q-WWjJgybtT7YNZytuAvCSDg7iXtS4xHhp3LuNAdwLIroV1_um4VSYYouDVmwGnOv_PwhZaujQel5oTx14z8wmaW8IFelQPhtvqG9w/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5380408047005584290" border="0" /><br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilonsPIL_UD3bcuBzFIH9mStT4lvkwdMUyA0OoLxxKbA6aCpYrqC7DSAzpdgO1VhCmrItHTkwwKmX0SFCO0mpF2_up1OFskx04VXkxAEZPOI2MeE4wXJ9gbMrrXrrENV3jWFFviDWWKtA/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5380408791944985922" border="0" /><br /></div>Karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqbNH7bpSD0Da1lo7Q6EkSjCsrDePOxYnu5_H2N8N8_FI-w6X4ft8VRk2eCC9FfatVJN6k1xFO4kX1BDF94bjFCs08w7Xhohyphenhyphenaog9pC7cd1_lJ7RigEJKCRyRXKdDr1yqY9hPmfVLmhRI/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5380408781362281474" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9AAzV80xintfVT9MiLUmXfLDHr0OkjnzpbpTiBJ0G62LxUvDZzb97LaSqOAl_11DyKKOMPUimJpVBvgPR-wBl7lanUq1AXpyfkisqH8zC4bi9v7sCp1YwOX6JTDEN7yMZsKhpmCCBYE8/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5380408790640815778" border="0" /><br /></div>Karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJitiHBKMrE3JPYP6eC8wZhYlJ8mDsg03ZUZ7T9Mi95yj_M429NbMoVAvt-1WX_rMqoMEdFs42O9VVQ4-8yJrodma7J4QqVKBDjpCr_6u2A1NjOcrAjFugK2YUYxDtEuGiU4Y_X0c65ps/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380410124463896386" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjiZ6CNqFsUnn7-fUQSzx9NDyiui4aK1H9V5M6E78QgBUxQ3F-XUoi28MElzNQRBX4i-sDSvoUL_MslJBewApsaWHVu2bK5KqnodIT6Wt_hxTrlUUY4UFfxA-X9zZc85nMpqVW0GQ77vY/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380410114569340338" border="0" /> harus lebih besar <span style="font-weight: bold;">1</span> dan harus lebih kecil dari <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" />, maka ini mengisyaratkan bahwa<img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJitiHBKMrE3JPYP6eC8wZhYlJ8mDsg03ZUZ7T9Mi95yj_M429NbMoVAvt-1WX_rMqoMEdFs42O9VVQ4-8yJrodma7J4QqVKBDjpCr_6u2A1NjOcrAjFugK2YUYxDtEuGiU4Y_X0c65ps/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380410124463896386" border="0" /> = <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjiZ6CNqFsUnn7-fUQSzx9NDyiui4aK1H9V5M6E78QgBUxQ3F-XUoi28MElzNQRBX4i-sDSvoUL_MslJBewApsaWHVu2bK5KqnodIT6Wt_hxTrlUUY4UFfxA-X9zZc85nMpqVW0GQ77vY/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380410114569340338" border="0" />. Pernyataan ini kontradiksi dengan asumsi awal bahwa <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJitiHBKMrE3JPYP6eC8wZhYlJ8mDsg03ZUZ7T9Mi95yj_M429NbMoVAvt-1WX_rMqoMEdFs42O9VVQ4-8yJrodma7J4QqVKBDjpCr_6u2A1NjOcrAjFugK2YUYxDtEuGiU4Y_X0c65ps/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380410124463896386" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjiZ6CNqFsUnn7-fUQSzx9NDyiui4aK1H9V5M6E78QgBUxQ3F-XUoi28MElzNQRBX4i-sDSvoUL_MslJBewApsaWHVu2bK5KqnodIT6Wt_hxTrlUUY4UFfxA-X9zZc85nMpqVW0GQ77vY/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380410114569340338" border="0" /> harus berbeda. Jadi, terbukti bahwa dari barisan itu tidak ada dua bilangan yang kongruen modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" />.</td></tr></tbody></table><br />Dari kedua argumen di atas, maka:<br /><br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGqbDIffYh9ohPhA0uslppQdK3jpf8p7I0SYvxrwQKHszHg0lWUgUw0MPfxIZGt27LHEOBabl41pBM4mWjpkJ1ZsSqh_A1fErImPYAHOsIuA4eXsRXv-aX13vbQ0e24b43Dhd0bN9XEB8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380413265677889282" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjM2Z0E9Khfby5WsySN_4AGnkzrW2jQjee8ZxlARKEXbqL6-f9M8xzxf6lZTDw5KejyGtymSEqGJWTsmR1ZkYKG9hNLB0331u31Hot9BXFZxDDHB3W0kz5_Q30FPV1ZCg8OxwGk2lduZjc/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380413254444395618" border="0" /><br /></div>Karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhZwaqe-V25j1pz_v9WnCzlMTQO8LjT5mWH8wYh6jzR-A5oJp4bfLygD7jBkNEtChNDDbXomhW6_Sdw7qh6dGOqPDNLFLVJNcm4vKAGyLnu5ktXw3f9ZRMbz93gMkPw-Y4KlLt3J_55HI/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5380413671868850738" border="0" />, maka:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirzmEM9Dn89fB5nIEXRWKBvIUCQs7zk_9_4eEXGBp2AFQfJwYwDLEGgYUd2jaJmlw8B4477-FJiqaSRSW83BC6e126nNb6BIH_THBimfbwjYnVSfYldMY29TmAhqNW4kvEllYguyK7ev4/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380413247802396626" border="0" /><br /></div><div style="text-align: center;"><div style="text-align: justify;"><div style="text-align: center;">TERBUKTI. ■<br /></div><br />=======================================================================<br /><div style="text-align: center;"><img style="vertical-align: -8pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjz3GZdz7_mJ0Jc0x4aCs_9cXJBMYGvjKpa0CEu02hxw6uE6jMZEd451SHKEvc7W4Y0E6fvWRXvmGvHWxwCJTPwuS68KiNz9uBIrRw1SoO6OiIeCegthky8WJFxOLNvTg2BwBWbDO0Yf74/s400/judul2.jpg" alt="" id="BLOGGER_PHOTO_ID_5380416809373931154" border="0" /><br /></div>Selain bentuk di atas, Fermat's Little Theorem juga mempunyai bentuk lain.<br /><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 30px; margin-right: 30px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;">Fermat's Little Theorem<br /></div><div style="text-align: center;">Jika <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" /> adalah bilangan prima dan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsLikLpa-_rsbOShQ-FoFhnVQL94awKhj7_9ddOn9A4Vgp9rOlHb53ROyBOw-GS7YAC_GFEvoWKRIsjAfAhSWP4q0y7105fmvaBOEY3_hnW45O5kTAy5G7gxjidr-nS5oKIeEm7vl36II/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380389911748218162" border="0" /> adalah integer positif, maka<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZk7VMpNjkM1Xe5iHe4lDJU0B2lb0L3k8Axq3U_hJcc2EpBQl2vrjVYHt8mhhvjMKDBVLYWCx8zDJmF-jc_LGpaURTqH2vRfp6fVBA8IMoO4K3T6KAI0SilVRxVtsUQyeHG_MHmeskTFs/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380488185006589730" border="0" /><br /><div style="text-align: justify;">Note: <span style="font-style: italic;">perhatikan bahwa </span><img style="vertical-align: -5pt; font-style: italic;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNXRJRHISzhYQ_Vae880EQq2xa3tRAs7y0Gdr59bNPPxjd9z7NL2gpupAnaawumWhv31-LBTxdku9ahD7sIzw4PiQrgzLpX9PVqxB5o4JRxT0-MA-fgcQfiy8XbzwBbItOKE8N9VXZC4w/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380390364084163426" border="0" /><span style="font-style: italic;"> bukanlah syarat wajib.</span><br /></div></div></div><span style="font-weight: bold;">Bukti:</span><br />Kita pisah menjadi 2 bagian:<br /><br />Bagian 1:<br />Jika <img style="vertical-align: -5pt; font-style: italic;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNXRJRHISzhYQ_Vae880EQq2xa3tRAs7y0Gdr59bNPPxjd9z7NL2gpupAnaawumWhv31-LBTxdku9ahD7sIzw4PiQrgzLpX9PVqxB5o4JRxT0-MA-fgcQfiy8XbzwBbItOKE8N9VXZC4w/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380390364084163426" border="0" />, maka teorema Fermat bentuk sebelumnya berlaku:<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5zMtSrBLQesP0fblXMpd9OEtSN90LhdNm8aDoJUz1mwPobxdGkoZXqQNxKYlXhzRj2j3zyX3h9q-p-F4zXJzwpOyEYDCqJS0Eu1BI1y_Q55xg28H3vKarzto5fyeumyJa2J-5XwcI-jg/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380389898829856338" border="0" /><br /></div>Kalikan dengan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsLikLpa-_rsbOShQ-FoFhnVQL94awKhj7_9ddOn9A4Vgp9rOlHb53ROyBOw-GS7YAC_GFEvoWKRIsjAfAhSWP4q0y7105fmvaBOEY3_hnW45O5kTAy5G7gxjidr-nS5oKIeEm7vl36II/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380389911748218162" border="0" /> di kedua ruas, maka hasilnya:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZk7VMpNjkM1Xe5iHe4lDJU0B2lb0L3k8Axq3U_hJcc2EpBQl2vrjVYHt8mhhvjMKDBVLYWCx8zDJmF-jc_LGpaURTqH2vRfp6fVBA8IMoO4K3T6KAI0SilVRxVtsUQyeHG_MHmeskTFs/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380488185006589730" border="0" /><br /></div>Bagian 2:<br />Jika <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2He4DF0wTbLpe89_mn5HFJpb0z0QJo4vR2oLqs4-904nJ5SVNtePnF1UJ68BwxFUrm_VLzvD5HRdYRLTuobyyHhukCeLMP9XzZX_QSdxsiHtQs0Muv7QrR-M5KcBQS9M9kX0FyJMm6mI/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380490307253597650" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-CTzbYNtJE5g8AiNVrkPegIQYAT7FEVON-5hZ7Bh-BmGWzDHubOpCSbytXsYLh8deRqYVcaBSyZUkTpNVk8LNVDgoEjl-opN2cyRTsxFnJovuMNb7IOzK7GAQUX0SmVFWzi1JqiRMUQQ/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380490300616837234" border="0" />. Dengan demikian, teorema di atas terbukti benar.<br /><br />Jadi, bentuk lain dari Fermat's Last Theorem pun terbukti. ■<br /><br />=======================================================================<br /><div style="text-align: center;"><img style="vertical-align: -8pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgySDuywI-5RQr_KRmz9XB23UKjxqsKQbFGaG1QZLG2COzRlhiyP8D3y8V7cznoYiD5tsVsnwRdU-7WaCV6ydRGvqX7itplJ5hFiooc-penKn_pn47nT0qDnlmIG2p3aAQm90c9p3XSAoQ/s400/judul3.jpg" alt="" id="BLOGGER_PHOTO_ID_5380491577090552082" border="0" /><br /></div>Bukti secara induksi matematika memanfaatkan konsep teorema binomial.<br /><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Teorema binomial:<br /><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg66b2Lf1RvyBdx9LWBV2xF57IbKTzsf03iA4ZMtVoRsxuYpIlVN9O50Y4X6sFXlvhYJy-i2DC4HG7TR2FPtEVfLz1NmJA9WiWkLaORkNBg5BlX2rv6GEU2nwjMg5jRnwwK_85xmzhcdN0/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380493739330751122" border="0" /><br /></div>Perhatikan bahwa hanya suku pertama dan suku terakhir saja yang TIDAK habis dibagi oleh <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" /><br />Oleh karena itu:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrb8L2Y3scaxH4881UestiBoB-M44i6DyG_TWo75LjSXRUdc1yEZ8AO6hk3DmKakqu-YgR4DuFv4l4Xy48kxycYsBoIc1ilD8BD4WyBb4PwEpKuVKgpO_OczBIIfT_7W4_0Y3b_Upike4/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380493730597572754" border="0" /><br /><div style="text-align: justify;">Note: <img style="vertical-align: -3pt; font-style: italic;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" /><span style="font-style: italic;"> HARUS bilangan prima.</span><br /></div></div></div><br />(i) Jika <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2yxtxtET9NPTItCiK1Zr1IRTGyhbjGwnoPbLrHCh3AwMNoDNoVUuKXgcUEyoQ3OzdpdkEnZM0FmMl0DkgoSlo5msyRgy9SnxKvh77EDMHHhLULJtC8InqoahgDaxtcKzxNfLDU06NCNE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380495166427930754" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTzNz4xfmuvZLXnu9w-HVAA70ttwDADj-jg_GtDSQkEwI0OA3whMIPvSXnzgHUg_JGjlNpJs9fZFryRMHxz-l7Ceqh3FWZi-MwBNTpxX0WiDvVoAyEAtDC3VeiTOpdVr5KqYL2oe6tRWk/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380495470086167458" border="0" /> terbukti benar untuk semua <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5CeiMvk-bk9o2jwARjz0am3UOLaWgJijuQXwHLcgHGMF_k2aYTK5QRCgug5Og4_8kKehJI7zJw1E3PSBlrthsvf02d_xSHmz1une24ni7_KuqU1BYEubHnITJzuMs6SO1kwB2Som7uYw/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380389922864081154" border="0" />.<br />(ii) Asumsikan bahwa untuk suatu <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjo9XaPUC2R2YGrlGRnUVM5XGSZSL-8FyG2LenabG_upvC9Je0jdN_uXJIewFZrgD6BujGvX77yoD2cxetqkYeYw8WnaafiOa_7Rd3kaKua0TcroO74KvznVwW2M_LZz9Oi85uVP8acmJg/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380495803013517842" border="0" />, pernyataan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyd2RL5yM21Cl7MxmNkFfmYfy_kO3Z_UU7C1zjC_3TJ3qoosW5hqp6C7DVMuH5s2_OP22LhZjDypkU-EQcAMiRyCRnBYxUCHIuGtL0h34ZTpz1ClslvL3HLXgvu51E2w3qs-kiU72U6_s/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5380496056816131106" border="0" /> adalah BENAR.<br />Dengan demikian, kita akan cek untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgviBtu3d1KMLWINSshkqTLutx213_UaNj5fcIjI3t8EB14mr15GhFoQ53K-4ORYihtKMJ2nGlLBXba0D-qW8FH-e3-K73r_6naExmY40EyJ_0jZnj5lOo-4UtNVHUyAE2Y60h5Rl3fz8I/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5380496885660510178" border="0" />. Dari teorema binomial, kita dapatkan:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSn_iF_MyzYokVRg1_Jt2Atjni5g_TLiSxg8veIxhBzeyUucapbPw0ZLPG7vppXiM-8MfMnANzrQS-nE-zYbrfYVuoxfn_1C3fMlNuNhB5DrIQCfFqmLBVrG_EWdiXR_-7kDoskMa12Ug/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5380498712324646114" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2tukTypQu9slLtBM1yhTAG1FQpSq1tI3wPTE3VDHxTaNoSh4y0U3mIjO8_W3tfDROyx8WTLYpT4l44ElCBTzfps1un2i6AJ9s3Q_Qoaazk_yIWpa5hG-qWqeKX69okDoe0hkIuPHoDbQ/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5380498525144520130" border="0" /><br /></div>Dari asumsi sebelumnya, dikatakan bahwa <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyd2RL5yM21Cl7MxmNkFfmYfy_kO3Z_UU7C1zjC_3TJ3qoosW5hqp6C7DVMuH5s2_OP22LhZjDypkU-EQcAMiRyCRnBYxUCHIuGtL0h34ZTpz1ClslvL3HLXgvu51E2w3qs-kiU72U6_s/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5380496056816131106" border="0" />, maka:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOhss-x4yhK3f15y58qCShw9ZFD08w5C6VWc_xMe1JkXIk9qbEgXOiEJP0zFjKab_Gvvc_0qJKSAM4n34vVdgxjTw3LLe4fXFghCZDq8RYdONUuNZ1wZ_ocZvYRDWZQad3ru1hPfoeXOU/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5380499103052861922" border="0" /><br /></div>Maka, teorema bernilai benar untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgviBtu3d1KMLWINSshkqTLutx213_UaNj5fcIjI3t8EB14mr15GhFoQ53K-4ORYihtKMJ2nGlLBXba0D-qW8FH-e3-K73r_6naExmY40EyJ_0jZnj5lOo-4UtNVHUyAE2Y60h5Rl3fz8I/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5380496885660510178" border="0" />.<br /><br />Dengan demikian, Fermat's Little Theorem TERBUKTI secara induksi matematika. ■<br /><br />=======================================================================<br /><div style="text-align: center;"><img style="vertical-align: -8pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhspAJ-mBQx64k6Go9E4kbm9lpi4q0HhSjEReAygwkyzI8UqBuRSfutY9U6JxP6cXw9ThDcXd1fZDzcs0ss4dLF7v3Ygzp8-LDYAYULhDnMFcb_s4FFTMTuE1tTmsKeLo1Z9k1weFgqVbk/s400/1.jpg" alt="" id="BLOGGER_PHOTO_ID_5380500065479753954" border="0" /><br /></div><span style="font-weight: bold;"><span style="background: rgb(235, 151, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh Soal 1:<br /></span></span></div></div>Tentukan sisa pembagian jika <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE4Gze-oxlgs2Hld8PuO93Fupbjw9wqrirpkzebxvAg9RNttFC4wd2PLiZXaca91Bx-LlKQdxyErVFjZ2ozhpoU0hnhRUCEG5cUesqI8a0vcLf1aHkLafg-4YMHeLl_7SYk5q1V5EZQTM/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380500780202778706" border="0" /> dibagi 73.<br /><br />Jawab:<br />73 adalah bilangan prima, maka dari Fermat's Little Theorem kita tahu bahwa <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOhUWAVTizAM4ihi3tGVh9YQGEkzPT35Qq9-87rXVAvBUOfwhbtQAcqKS7HQmdOGeoA2HxsxW8gTEHw5BjQoeBep-3K3p0nJgf2PPqcKiACdmQMi1FEnwT7M_x0-E9vfN4uhdTxDG36eE/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380502463050132834" border="0" />.<br />Maka, kita kelompokkan berdasarkan 72.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE4Gze-oxlgs2Hld8PuO93Fupbjw9wqrirpkzebxvAg9RNttFC4wd2PLiZXaca91Bx-LlKQdxyErVFjZ2ozhpoU0hnhRUCEG5cUesqI8a0vcLf1aHkLafg-4YMHeLl_7SYk5q1V5EZQTM/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380500780202778706" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbQEX_j1RB-qVcevDAo2XwkamToNkAnL5bj8nhLTUGlksCb8WxdAtTvSm8SgbK-cX08-JjG3Q4KSywv7v1hKdS0GyRU87wcr0ihXI1W8i7Gl7w84uhCOhnlLEf3jzyDVpxdwPS6mPMr6c/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380504374959003010" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4PxliCKEyI_cW8c6r0j06XVtXmLF14riCuvgLX-UNTklii1JCorLMwrVw3Npz4w2GVsKc5OQNXR9CEnMgusoYAiGzc7p1uh6VyvSm-brEY4OUDhW4HeMGpWlZgxXokYIN8AoxfuRokK8/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380505052448894322" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOKBUApqIN8pV2jznEZSk5rhcUZod1YdssigrazCgeAvXzEd70AIrbZJ8XIUJeA9C2PyLr70Ewo_w3wOnU7q8o3y9y3RkwBkEJbI8VNsWfnVEZQDt8FFXwKvsYzp38XoSxAZx0nAIFV94/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380505044394705762" border="0" />.<br />Selanjutnya, kita gunakan cara biasa.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOKBUApqIN8pV2jznEZSk5rhcUZod1YdssigrazCgeAvXzEd70AIrbZJ8XIUJeA9C2PyLr70Ewo_w3wOnU7q8o3y9y3RkwBkEJbI8VNsWfnVEZQDt8FFXwKvsYzp38XoSxAZx0nAIFV94/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380505044394705762" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2wPg629ESXBuHC9HcVdD4P_vlCZ_o3dPV4tDMAW6-IwoWT3zHExxGAvYzlhnnsKh0TUjkOx-WNVQGKbcMzFo1rbQmwcK3v_Ibs-r2rxZzMajb11IbGO5AQrC4BGfCiDHBrFeQTGC83Nc/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5380507506362530194" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-XEbdslVNKmHoLpTvyL0juG7uRaAGgl_nNsU6RwL7Ypfbh9r1k5MYJJg1hJdaDHIrQt8SAGe8q2wNiF-sk8c-ETwb8v6L4mCFonjoJMdC3KmsvD4EOAmYKP5o1XtrA4DS1turM1qWC8w/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5380507494873243698" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgorvyZRGkdeCVl0vLXTH7OLXTo6lg324wOE-ykpFFqjACVHPbcUL6YA35Q-OiIhVlddlhRN8FQ1DoYWLSKTn05eJ8W1SPP-oiFSmthK_rBgbGdtJixaVdNs0RVBphcz9jZInQ538EETrg/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5380507345659302338" border="0" /><br /><span style="color: rgb(255, 255, 255);">____</span><span style="color: rgb(255, 255, 255);">__</span><span style="color: rgb(255, 255, 255);">__</span><span style="color: rgb(255, 255, 255);">_</span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikuSNYWe2R_gDsX_KuyqUw1VCeKhNNSHCyTwg3RQzgkeFzZ8MU8dLHroh19r-B7lCBbIBIaEdV_urb4R5UoQxIkfJRJLmAhhtvxgfPInTM7zxx_gjZp_csmo1w4wbtSBEPPF1a72e4kQM/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5380507337286683810" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgF7v8Y7LoIBoYg0msdUykAYifyKJSEv5oxOtUfA8F2l_1fOtst5y4S4sU4k_1x8b0vIxM2mpXDwUlgm7CqBgxx5bXfWgCfFyWnwVTJAlswIbbQrEM8faZ1uvPO8UJ_15zmk3eTG_HnHYk/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5380507333936189842" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_lzrC1h4AUq73c0Q18u3IYznTY6gW3Br_h0LpKtBSir9S5ugfEKGQR9a1GRTILG7ZgFM-VyEBhIhLxCGrGwnRi71JN6Fw8WTY02bEKd918mDrsig54-bVW36M0rbr6DDTjyEiEFby_Is/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5380507325356745202" border="0" /><br /><span style="color: rgb(255, 255, 255);">_______</span><span style="color: rgb(255, 255, 255);">__</span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS-0uuKHP53O6eteS_tzWxSiGOf2W9tgPR7nuvLKMVVx1FUBqap2XGAULfP4VyIKpXixGTYStcUEVpF_ugMtp5pO9C6y8yNq1wfybdq34F0sSJ3i-vLk18hYzJB9sfpikPixt_zuj87vk/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5380507318504348978" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVjfERcMR89LCH2_S4-ZzDp33RsmfLf60gfXMcG1e5uKyPkjKZqs2MX7-sshR0ZUM3YvH-Okr-AcNky5hKB4bI-COZqQRA07ctp9tOSLsoquR2ihfo0rNVjIeynNKgMfJxTIlkaMoGMVU/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5380508414421863042" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEha9ZQjt3ibePT37_XStD6VDef2lcTqdK9t9Rv-8vXAMYINF23tOV8AWYpXpNWatDtNPOmSTqsSP4MD4vwEyGaQ3DEX10-LXZ12PUZQn7y4jI1qayxqsYoiYwmrd5GC_XDT1dQNIOgiLzs/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5380508405590407906" border="0" /><br /><span style="color: rgb(255, 255, 255);">_______</span><span style="color: rgb(255, 255, 255);">__</span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6GiMGdKBuGusWbdB4AA89qQnyuz5K-qhcD5YoMHZZqCZ63A5apJq4VrjN7MrJ8euHPptAoLwO-NINsaZSlNzG3gK6cKh0FiIBPyMkvAnD_iR8jg4mADROqtmVrTh_89v9gpdzIxBA7Rc/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5380508398025036642" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgys5m_3rhJdbT4m_ckDNDGs1hsTkFZc7kmLpRpwVYuPqFWnoGtMPe2DoTzpzjJTD25sl9lzDEQbMXYWhyphenhyphensi1wF6oPG0CkI4GI_0QO5dLygv5F-VVfTsWucnpVz6RcZjcQPxdKHRv0dyxI/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5380508392555910722" border="0" /><br /><span style="color: rgb(255, 255, 255);">_______</span><span style="color: rgb(255, 255, 255);">__</span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDnoRTlYrbxnq53qdd0iQhZmsbDQxVioHDDq1OCxobseeSECXZ1wF35vS7lb9p1laIoWrb6P85e1ggSNPXIHiVwhs0T16KKd-FRYJQihBxGVkJiW4yiIW1mB6b0x9PsB-FFPD4rhekrjg/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5380508391499888754" border="0" />.<br /><br />Jadi, sisa pembagiannya adalah 32.<br /><br /><span style="font-weight: bold;"><span style="background: rgb(235, 151, 100) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">Contoh Soal 2:</span></span><br />Tentukan invers dari 6 modulo 11.<br /><br />Jawab:<br /><img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsLikLpa-_rsbOShQ-FoFhnVQL94awKhj7_9ddOn9A4Vgp9rOlHb53ROyBOw-GS7YAC_GFEvoWKRIsjAfAhSWP4q0y7105fmvaBOEY3_hnW45O5kTAy5G7gxjidr-nS5oKIeEm7vl36II/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380389911748218162" border="0" /> dikatakan invers dari <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzhQrq25x2CKxYbQITi8ZL2H7ErinhYil5ru4-zEndnALinqW8Q56G3QN9TqewT-S6KHu8ivFDfoxU33q8A_QPahdyTiftlpWf3qDsXeYmpvNDCnVDmzsOAUNJs8tEEu_WJBpWk7UrwqE/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380511618484210354" border="0" /> modulo <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO1Wqj1zGvWstsRbGh4r6x2sP0P-2n4KLiWEu8qNhLlA2dliN6V8oe-blJBRV7NdYiXBIQdyrzXBKn8LfUandNJccTiklmb_9Jkw8zcVKVeCZW9Nau6giiW4skt4HNpEuPummDLExUpNA/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380511612714845074" border="0" /> apabila memenuhi <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvCaRtmeZ9bmhhk2FYiVFHe07JKGcOzU7PXToM6RbYxIVQrhgHQ2VHFWMTywa13NZbmMd5GJLGjIE2I-HeQzNvTcj1rea6efnTqhEkptDbGCkEgaA_yFrnwyZOQVINNdxzeIPTYPWXwm0/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380511605859588738" border="0" />.<br />Kita dapat menggunakan banyak cara.<br /><span style="font-weight: bold;"><br />Pertama:</span> coba-coba, mulai dari 1,2,3,...,11.<br />1x6 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> 6 mod 11<br />2 x 6 =12 <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> 1 mod 11.<br />Note: karena modulo bilangan prima selalu mempunyai invers yang unik modulo p(Lihat di <a href="http://hendrydext.blogspot.com/2009/08/teorema-wilson.html">SINI</a>), maka kita sudah mendapatkan jawabannya, yaitu <span style="font-weight: bold;">2</span>.<br /><br /><span style="font-weight: bold;">Cara kedua: </span>dengan algoritma Euclid sampai tahap Bezout identity.<br /><div style="text-align: left;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8TT3YhUVhNThinpodztyh_43esLHQ8Tdq2VI0gWvuwsa6hRmWD9S7LG-_8tR-yCaib9DzhEh_YzcGKMMnm_tc1l7L2wpd8HYY55azlgqq60TDSmHDHnkr48YjDqftQcWH5EODrwXCJkk/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380513791089385938" border="0" /><br /></div>11 = 6 + 5<br />6 = 5 + 1<br />Jadi, 1 = 6-5 = 6-(11-6) = 2.6 - 11<br />Bezout Identity-nya:<br /><div style="text-align: center;">6.<span style="font-weight: bold;">2</span> - 11 = 1<br /></div>Jadi, invers modulo-nya adalah <span style="font-weight: bold;">2</span>.<br /><br /><span style="font-weight: bold;">Cara ketiga:</span> Dengan Fermat Little Theorem (berlaku karena 11 adalah bilangan prima).<br />Fermat's Little Theorem <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5zMtSrBLQesP0fblXMpd9OEtSN90LhdNm8aDoJUz1mwPobxdGkoZXqQNxKYlXhzRj2j3zyX3h9q-p-F4zXJzwpOyEYDCqJS0Eu1BI1y_Q55xg28H3vKarzto5fyeumyJa2J-5XwcI-jg/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380389898829856338" border="0" /> dapat dimodifikasi menjadi<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKJ0rbhfdpkGBHuCwg8jopSFrE9cXsRsCeuvaSgSBenUXASjfH2pm964AQqQezIirlW5o368kagyUJ5UhOFq2u_9AgbmAr5uAGRAThwq72oQ86bp97Go5tC36WVT3oDyXAC5UBTJle0Fc/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5380515533395837714" border="0" /><br /></div>Jadi, <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip7IRTYqab8cKSKuL37V8Sr0lF0SAwx4HcdOTBzE2Fyh607hJhSArvrw9kcy89LNTI9Elkp4rBUuOWmTm_6XmNL9Mn9wLEFTOOM-LWXOqKhj5IIONdYM7YIFVjPAOwbwtZ9JwTq_MOxns/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5380515524568922178" border="0" /> adalah invers dari <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjL1k1ep-LdAZV3VMgTqThB1-7r0s4OdIDJSzamuqnFCmUDGBuxaOMuO6ADBDHzjaFQYBEwKVfR3rt3Z2h5h2OsQvfjnRIwWNf8usvHJZSm12WMKBMaKjFvT719_xiomunID_XaVnRBg4I/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5380515844718964098" border="0" />.<br /><br />Jadi, invers dari <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrM0-sXAd7w3sQYkL1QoFNJtQIjD99CNN4rxLtQDcP97WmHuPxLQKqAKO9Z_0ZsA9PDtgUf591ACtObbkzc_YcAKBwMt6u1vsFByJCKtjgFkhpWwtjXYrsoGxSO2VsaIDq_9SCQSooe44/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5380517067125472162" border="0" /> adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBpWwvuxtnuFdYsqclbuWoLnD5FzcCB_2HG2WKf8Iqg18uFHQLZEFY1QY0cPvF1VKdb1tX57E8rPCllRNSBnuwEkSw05tCqB45JS86eUIKgRBsEEsy1ZBRgF-YnKEyva9jzcwARYc1NIM/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5380517061370751714" border="0" /><br /><span style="color: rgb(255, 255, 255);">___________</span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk2Xd5KT2oKVierKn0smNa9m7DaNz7LY2M_Q9OF4SQ6NnLr40fTgj4A-A1zxERCn_e1mqk0Br0cn5PLXBO574hQKTnYn_4DibXeGsvvqNMNAILJyGTvBHhaWQ6IvoCFbh1osECicNlBwU/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5380517899268571682" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi55L1_2jJnsKIXh5_0PbOYmFlUsdNqSv-vaP4admnDFYiX5QQR1wjcPj0_VT-V_bQty_4o6da2hyFDEvYQwMBAsw0tL7CwwfwkJsr6fU6jp-LNoAVkEHoa4ymypX7DAAE_TQEFBch_vKk/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5380517896146251922" border="0" /><br /><span style="color: rgb(255, 255, 255);">___________</span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHIvtBnR8hcf826I3mwTnb_5V9XEmGVfYc2qMa1YPOl_kW2LYXSG_qRriDexvFnHJKh5f7BWA9LM9weYb6sqH-eBSOs25D2ZbHkW8Tdit0OMoZSsEIbPWgGkxS8GX8mN54BhcquiuKuNc/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380517886199491042" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLBNBb3dA4z_hRFObPMyam7iR808wf62tIOdhYDqj0GZGsy8u2ghWamJzR1PjzntqczUAoc5hyphenhyphen0nbMRNwqPzfRWuGYbxIZDusLpwLIOD8JnDuWirDJZsgyaGVDITwn0QfVZdl3wd_1Mo8/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5380517875544921122" border="0" /><br /><span style="color: rgb(255, 255, 255);">___________</span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnQUQAAb4MKIFszGgme5yYxDkQzcyCwRdQrqQ7BsRYf1jCDHNFJe89o5U3SQJGBTKWKErjbENvpdhzwLUEG2VT6T8EitpQB3SkbA6JX6p941iVTFBfOuDAHRy8luzcp3n4gJA4xfi3suE/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5380504638423215090" border="0" /> <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZ_82T-AvDiuj6PaK2lW5pSZrIuIazw8c5G75FHD40Cszi_wKFKuIZw8t1NjDwOYF7NlRgnVqi_2I1Uhakc6sCyuyAv7F1HmQVHTwlbdhUnqAHzR536750bkq8KA5edwZgsdUdQQ4hE50/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5380517870621240994" border="0" />.<br /><br /><span style="font-weight: bold;">Cara Lainnya</span> tentunya masih ada, misalnya dengan euler-phi function. Lihat di post berikutnya..<br /><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyCLUjB0lsW5acNwhmWTyuuIkYn8K1KSMvVGXfJpdH0k_G-xfIMhO0h_OXG8n6jgEpxI4SuIxNPbQ5l5Xq0Uk4YD6sgNgh3Bolj4AJxZ6Zsx3-EBN-olN8MBECvuA-YO0E7auljnKPBLk/s1600-h/judul+close.jpg"><img style="cursor: pointer; width: 83px; height: 28px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyCLUjB0lsW5acNwhmWTyuuIkYn8K1KSMvVGXfJpdH0k_G-xfIMhO0h_OXG8n6jgEpxI4SuIxNPbQ5l5Xq0Uk4YD6sgNgh3Bolj4AJxZ6Zsx3-EBN-olN8MBECvuA-YO0E7auljnKPBLk/s400/judul+close.jpg" alt="" id="BLOGGER_PHOTO_ID_5380521116394763442" border="0" /></a><br /></div><div style="text-align: justify;">Fermat's Little Theorem juga memiliki bukti-bukti lain, misalnya <a href="http://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem">dengan menghitung bracelet</a>, <a href="http://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem">system dinamis</a>, dan sebagainya. Namun, karena <strike>saya sangat malas</strike> keterbatasan tempat di post ini. Jadi, sebaiknya kalian lihat sendiri di sumbernya langsung, yaitu di "tante" <a href="http://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem">wikipedia</a>. :P<br /><br />Sesungguhnya masih banyak yang harus dibahas dari Fermat's Little Theorem. Leonhard Euler mengembangkan teorema Fermat yang digeneralisasi. (Lihat <a href="http://hendrydext.blogspot.com/2009/09/teorema-euler.html">Teorema Euler</a>).Kemudian, adapula algoritma Pollard's p-1 yang didasarkan pada Fermat' Little Theorem ini. Kegunaannya pun banyak, misalnya untuk tes keprimaan (menentukan suatu bilangan prima atau tidak), dan sebagainya.<br /><br />Tujuan post ini hanya untuk mengenalkan Fermat's Little Theorem. Selanjutnya, untuk pengembangan akan dibahas lebih lanjut di post-post berikutnya. Semoga post ini berguna dan saya harap post ini dapat kalian mengerti. Saya tahu ini memang bahan yang berat, karena harus mengikuti bahan-bahan sebelumnya, yaitu divisibility, modulo, dan Bezout Identity. Namun, akan sangat mudah jika kalian sudah tahu dasarnya. :)<br /></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber:<br /><a href="http://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem">http://en.wikipedia.org/wiki/Proofs_of_Fermat%27s_little_theorem</a><br />Buku Elementary Number Theory oleh Kenneth H Rosen.<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com5tag:blogger.com,1999:blog-8125318493233557109.post-39442688098729313392009-09-03T22:01:00.005+07:002009-09-03T22:39:21.934+07:00Kotak yang Kosong<div style="border: 3px dashed rgb(255, 200, 50); padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Ada 80 orang dan 80 buah kotak yang dinomori dari 1 sampai 80.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHXbUFiBhTOib5WcdwGzaAHePJPE4BJQKDgYxZ-yVceqJlthZuuHM3J8P3CTCOjMw729E2t3XPGew5H3HgXD2SvW24q6nJFanSP4Gk_v-dr_Q8T-iF5kiFj1rUzvZ1_Nu78IgKAA0DZpU/s1600-h/80+boxes.jpg"><img style="cursor: pointer; width: 498px; height: 52px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHXbUFiBhTOib5WcdwGzaAHePJPE4BJQKDgYxZ-yVceqJlthZuuHM3J8P3CTCOjMw729E2t3XPGew5H3HgXD2SvW24q6nJFanSP4Gk_v-dr_Q8T-iF5kiFj1rUzvZ1_Nu78IgKAA0DZpU/s800/80+boxes.jpg" alt="" id="BLOGGER_PHOTO_ID_5377261914503740818" border="0" /></a><br /></div>Awalnya, semua kotak itu masih kosong. Kemudian orang pertama mengisi masing-masing kotak dengan 1 kelereng.<br /><br />Giliran orang kedua.<br />Orang kedua mengecek kotak dengan kelipatan 2, seperti kotak 2, kotak 4, dst.<br />Jika kotak itu berisi kelereng, maka kotak akan dikosongkan.<br />Jika kotak itu kosong, maka dia akan mengisi dengan kelereng.<br /><br />Giliran orang ketiga.<br />Orang ketiga mengecek kotak dengan kelipatan 3, seperti kotak 3, kotak 6, dst.<br />Seperti ketentuan sebelumnya, jika kotak itu berisi kelereng, maka kotak akan dikosongkan.<br />Jika kotak itu kosong, maka dia akan mengisi dengan kelereng.<br /><br />Dan seterusnya, hingga orang ke-80...<br />Pertanyaannya: <span style="font-style: italic;">Sekarang, kotak yang mana yang kosong</span>?</div>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com4tag:blogger.com,1999:blog-8125318493233557109.post-8513006415009503942009-08-31T19:24:00.004+07:002009-08-31T19:39:12.699+07:00Teka-Teki Ambil Bilangan<div style="border-style: dotted; border-color: rgb(174, 46, 255) rgb(98, 190, 204) rgb(98, 190, 204) rgb(174, 46, 255); border-width: 5px; padding: 5px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Pada zaman yang sangat-sangat lampau, di Eropa terjadi selisih pendapat.<br />Bangsa A mengatakan bahwa<br /><div style="text-align: center;">14 diambil 1 jadi 13.<br /></div><br />Bangsa B mengatakan bahwa<br /><div style="text-align: center;">14 diambil 1 jadi 15.<br /></div><br />Pertanyaannya: Siapa yang benar dari keduanya? Mengapa begitu?<br />Pertanyaan advance: Tentukan nilai B.<br /></div>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com5tag:blogger.com,1999:blog-8125318493233557109.post-31350105630916044212009-08-31T19:05:00.006+07:002009-09-03T21:29:02.967+07:00Makanan Otak ... (xxi) {Faktorial}<table align="center" border="0"><tbody><tr><td valign="top">1. <span style="color: rgb(255, 255, 255);">____</span></td><td><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGdzJKndgLmz009LIkM7Xp8AXPXQGyIZgX0hldwlk4GzDCiJOj6sFn-cqbv929k7TYznR0WLnytB-_DiM77LPD3X-ROeveN7bP5eT5vWSHfrjcF8cu2sIwOGBvKhHeZuFgfq2Qkp_X9mo/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5376100468703077394" border="0" /> habis dibagi oleh <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimW8Omml2f0T3BQlK_6MDtWsaXwohdYUVgKfCyIUXajEtJso78IdWl7-sI40qCYBwMsmwMOE1mS-5gioCzglvra9sQDIPK89pi_CHZLaRY0C3pFOZUhWbK_rdqleMMcxa5pFAHHW4g-2A/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5376100460764485986" border="0" />.<br />Tentukan integer <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1VHyoBT5xTcnod4WRA-aKQ9v_2-moXpsyvOgjSVKIatZqWIYyAmvN6OWq5holEsc85KFvU-xfEDJSgzRcfHu8BFRSblDNNHZ6GJ0q_F6hGu230Xd0D9ZI7ugHmCb4ZzTmVIf0bR7dq1I/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376101439853705266" border="0" /> yang terbesar.<br /><br /></td></tr><tr><td valign="top">2. <span style="color: rgb(255, 255, 255);">____</span></td><td><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO5AVdLzPsPsLEZVzOtm9S_n9qqBX_Q_U1iJmkgmqb0xPB36lK-4l8BT9Ecu_xYuSF9IfGV5nJGzAYx1NHgMhNAv3Y-samj6_vqB_5AjRMlHhoK5KuCFRUDlGdm8NbaIwIdcgj2CnlBAQ/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376100481182179922" border="0" /> habis dibagi oleh <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPWHlzhkbZcSGaTyTijPf9x-BSRL6AE5Xh2_kGibxBgE1ZMpBvvxBNkXIQ8YqE-zobotBqPExor65NwIGf-jBqyL4wZylqsi_SZNcx2EHUGH58qifl7N3xtAQD7odqWzW9cJ5j5_N_HGU/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5376100473025781938" border="0" />.<br />Tentukan nilai <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQW30CBId9_NhMKL-Ru_sVRunlttt1LUhzwIonz6ePWA7wpfUOd1Ij1L0bSMp3nusxvjDjiM98q99va5FKPRPIo-fTYfN-U_9LyNYhNRywynqAauiT5PwtXTnE63qffS8Rkof2Hb8eJjI/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376101767287369890" border="0" /> yang terkecil<br /><br /></td></tr><tr><td valign="top">3. <span style="color: rgb(255, 255, 255);">____</span></td><td>Tentukan berapa banyak akhiran nol dari hasil perhitungan di bawah<br /><div style="text-align: center;"><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5jx3Te05GoDT4n-RrVJ_IdVoMjozC91F7BMkRql4e1F6GPCbr7ZcysLZs5d64aLDyNDcy_flARQhuv1g0iXiAj9TWxlCs881mfck86x5hqF62Z12J8utwHfSYLSJGVmR8iexleZIphns/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376100489622355282" border="0" /><br /></div></td></tr></tbody></table><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><span style="font-weight: bold;">JAWABAN</span><br /></div>Ketiga soal di atas sesungguhnya memilik tipe yang sama.<br /><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Perhatikan kasus yang lebih sederhana berikut.<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl9TuviRmuk8nGdRIFjNT8mk2fz8m4Tqao8wu3f0d8kwScyQ6r5Hmnqpj1eZL-bAh8I3g8qlo1ZTr60z2voClFfvzuMLTD4hGqnHQ_YlFRXpMXayiMDq-cBEvNvOSnvbDy8XZCthxJJ9Y/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5377232530108739986" border="0" /> habis dibagi <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_Me4Pr7_hKCYtEpgTaiRuCansR08aYruTU5mdvPozf2s0XZByc9Yb5UupFwegeI6BPVyrF_YeENyjsWsCNbuHHpvGy_WBgeNIk4CBGW2osz1Y5IIVekZFbvo3g8PKtbxycwZUPeSQTYU/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5377232525055807570" border="0" />. Tentukan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1VHyoBT5xTcnod4WRA-aKQ9v_2-moXpsyvOgjSVKIatZqWIYyAmvN6OWq5holEsc85KFvU-xfEDJSgzRcfHu8BFRSblDNNHZ6GJ0q_F6hGu230Xd0D9ZI7ugHmCb4ZzTmVIf0bR7dq1I/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376101439853705266" border="0" /> yang terbesar.<br /></div><br />Supaya jelasnya, kita uraikan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl9TuviRmuk8nGdRIFjNT8mk2fz8m4Tqao8wu3f0d8kwScyQ6r5Hmnqpj1eZL-bAh8I3g8qlo1ZTr60z2voClFfvzuMLTD4hGqnHQ_YlFRXpMXayiMDq-cBEvNvOSnvbDy8XZCthxJJ9Y/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5377232530108739986" border="0" />.<br /><br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXKfFZFELW-e4T4_lyZMrKK6McYxo2DmeYJVwXdENZZjN188I0uQLvQSgoZUWri7fjtwiQFe2CsnJ44WwVS0pxmu11E2Qgpj9EWRYfqqi1BUK3LdG3FDoV0EsvALCgA5OWnV9G2qla6Ek/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5377233012954606834" border="0" /><br /></div>Dibagi dengan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl3yKMe-7LKn9gLCRLxTAIWBk-Ux4w9e5WrA-GwxdzXKgmWEDc_qJx0dnL9cgE3k6Z21FG136Or1u2w4SVyewjsorU6gN3li_-kl47jDgS_KfsphWpVj_5DAcoiGpkb4TbbBqanhZK-rQ/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5377234813009898258" border="0" /> hasilnya<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPacQEKjH3JGuX6v-jmW32VPkGuZZTq4KRFrjdICMVobtlvB8AAeXWhmHNW-AttmTy71w9joUuNAPH1k0Gh1t5j8u-0pBxDVCkEVfiRJ_WEPkNNx07hmruNfPiOe9PfEPUXtc17xCeIuo/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5377234804804568402" border="0" /><br /></div>Dibagi dengan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhc9lgjR_LUE7wzDRE4Hmd86oqotkPxmo408xwdtmxQfnjmrKUg-zETcyT72uCJbE2eCYHPnq80EYYxbiM3gNbQRlOJ6pdsWwAxiQV-WLCJ4EzeHF-tahFGij9aYyVK0sGnP4DpaRvOSFE/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5377234618313106178" border="0" /> hasilnya<div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtXhhLEcez9QSm2tdmEMu5RVndkUC5dCxnZL1-ACfLpm1xOazZ8hlThBu2h7Gf9M1MKYPUK35HUipLiR3tD6qoy_AGGJh85WnIpkQz7ZRRvElfLGSw5jKRv2qHXEpP0xP1UFQ86XiWSdg/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5377234799401356002" border="0" /><br /></div>Dibagi dengan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg05rbUvroqpDBE9n79rHlnHKU-IrXtKZYvG3we4U_Ooz60P-PDLv2NX1CJecWxibhuOinX_xPVqE3SvzBcGDl_zGECu0APVa3I2iw5wxR0qZ1wfAh2-Bhf1SspHQgT6c8bpE7FoeqkbcU/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5377234610013569762" border="0" /> hasilnya<div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjadh6wsbwwzAAHzU9GrbhUxZh4ngxssGZMPgzLP0pPd7CqygzuthqxnN-Kt6XYQjCkYa50ls3xyzWRl8f6IKc6CW3CJz5WwIPrhbgkS-G8hrrjjgTA15xnEKc11X0CKRyFfp0LfjUL2MU/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5377234630406603154" border="0" /><br /></div>Dibagi dengan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtm1841uzGppgT9e3SI45RKl6QdZFaKVzovvA6M4f23qkUjBVjlBWaadD2_9hqGoNdzaP5RUg9I6AHj4VQEeevgH0lZwxnwNuWK05vkxiqch4MI-IIJIRlSqzJvIGFwBinFE09wl0yY9M/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5377234607318101090" border="0" /> hasilnya<div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimaWkQr9czVGUJfiv2x8FcvfJeqKcyIwYWcOD7eD9ypWs_1tCTVhBdZlH0Oda5FXJ_Fx9SiESP8TQ-gV8FldXk4zjniwSyj1lPQCqshbezhHZinOL119PrCHReQd_w142JV93KXfKFc8g/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5377234624248577730" border="0" /><br /></div><br />Maka, <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMxmjFFA11eST8qfF7ZwiFJL2jiEEBa6vC90_TZOUi_2Ofl_tXvaM14Ed9CYti5PUASPKLkqvyq8dupZoUqRu9FLYLpz5r0I8A9uIS_qTcsTQTpx0gaFzcPDWLq1H61nbgo3MWusIKD-4/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5377235723893565810" border="0" /><br /><br />Penulisan di atas dapat dipersingkat menjadi sbb:<br /><div style="text-align: center;"><img style="vertical-align: -40pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiv6dPAkBq82v6bqf4RHfJxvzINYlV9oAl__UO4g4KdBhTzrHNK8cPL1WO1_Qx0XtohKNGcscgQ3VGLPnK06zXcU7QATZxiB6ufpy8tmVtvsGtWPvWOJuH9T2fSy9hZFkQC3wbzO5wucyE/s400/1.jpg" alt="" id="BLOGGER_PHOTO_ID_5377237639955542050" border="0" /><br /></div>Bentuk penulisannya juga bisa sbb:<br /><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjR95KnEInogAKPMhPdVLioXdwUDb2T45J6-YWOlcOBsTKf7T_SaxCUKhyphenhyphencY_Wlp-EmhAT_syXDnK0YDP2Te_4_0ysJjxv70NCVwvorQYY9v7wTq1l1z8fPitJmvsvFwokxusyQi0nVCBE/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5377238003516388594" border="0" /><br /><div style="text-align: justify;">Note: jika pembagiannya bersisa, maka sisa pembagian tersebut kita abaikan.<br /></div></div></div><br /><table align="center" border="1" width="90%"><tbody><tr><td valign="top" width="5%">1. <span style="color: rgb(255, 255, 255);">____</span></td><td><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpKoNdN6af13LdW3YjOlhKCdusEa2RsjHqtyWWAxpyx2hS1eSBdZ8XHzTp07OVAVtTajasQ7FlnR6aF_JDjZ0Ao59VKVKA_xYilh5S960cg2vKgdCARx-LLpMDlkCCZI0oOot5j_Ytea4/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5377238653241021138" border="0" /><br />Jadi, <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrsrOF1XApsiELvjBOSLxTe_28huc2MssIhXwV8l7kpwHZPj0UCQX1HcEZKbroXhtyNWF0ZoURqX7Xw3Rl7B8hUOzsQfJobxCwm4eMlz5TLV4E5p6X6O_wwQyTwSp4srLDTJDrjR6hZYw/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5377238642806267650" border="0" /><br /><br /></td></tr><tr><td valign="top">2. <span style="color: rgb(255, 255, 255);">____</span></td><td>Kita mencoba menerka.<br />Seandainya <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOGufAOeIl8sE1HHHXBDV3KNCsUzeUqa5B-5KI8Stfae1fq6P4et8YAfTA6MipqkOkdM1yVuQf779sZduug7oxGCJNQgf48WggHBJpT8GkwT-q8FrhgdKeUMs0-6w12YomnBCNKA2UJGA/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5377239579475180962" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip-xOvfW6TCL2oxAtY7azBpYcqLdU1zhWTyinZhHEPSNzDd0kMlGBcLGweVOvWaq98dxChfj81-B8sjOj7eV7-7CVMou8yzfK9A2ykjUZy4vF9ioqH9KlC_eBHZWihD2199C1wF-yvrn4/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5377240661863774322" border="0" /><br /></div>Masih kurang 4 untuk mencapai 1000.<br />Jadi, nilai <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQW30CBId9_NhMKL-Ru_sVRunlttt1LUhzwIonz6ePWA7wpfUOd1Ij1L0bSMp3nusxvjDjiM98q99va5FKPRPIo-fTYfN-U_9LyNYhNRywynqAauiT5PwtXTnE63qffS8Rkof2Hb8eJjI/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376101767287369890" border="0" /> harus lebih besar dari 2000.<br /><br />Seandainya nilai <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi50GzIiMe0h6NKEloHhQjS6qIcUbJZGvHQOO83kNXgPG5FpTd5b8PHRZX8WFBt5-WDyKX1cexUGuZ0qY1PVdpFSSMSTeEU0vmGpH6Vf7JM9LfXjmPnBLMsWnBDXMiiVXI3OHRszIJF83k/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5377241187915993506" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmplTXdXXE2amG3GyjPNIgwRfxy_C3vkWWDlLMo4tg1oTuRTZI3KYuUVLV6kJp0IDoAqT48rSxia_QKt6MQZJ6jtoq3Ncy0nFqnYKzpndIeInjpAZDoCg8-9OADSuupugNvsjpuRsLLRI/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5377241892172969698" border="0" /><br /><div style="text-align: justify;">Perhatikan bahwa <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQW30CBId9_NhMKL-Ru_sVRunlttt1LUhzwIonz6ePWA7wpfUOd1Ij1L0bSMp3nusxvjDjiM98q99va5FKPRPIo-fTYfN-U_9LyNYhNRywynqAauiT5PwtXTnE63qffS8Rkof2Hb8eJjI/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376101767287369890" border="0" /> harus merupakan kelipatan 3. Artinya mungkin 2004, atau 2007, atau 2010, etc.<br /><br />Seandainya <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBw2_BXv_mIaVHOlCU3vwPB2rKFBoB9wI3ALVcBhZLrBH2-B7RZMq4JmMR5TRdC2VX8KXY2zyUBNAMTsOMcGaWIjdYfrIvxYIHG0EymLAdAqZwrouf-tHnccvR5l1nVrpJYXyu1lVCOx0/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5377243300244443122" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQXqCsGe2-lGuuiCn_zmyA0DhDZCsoQ_RWAEZkuD2A9EcXKzStVMLRxBS76w5742qmQZN7GDGKpmDTFrqrLtMQVboiv7guXNSb5PZtUYNcSCYzUCy1ycxWTgdBB07VlrRfDjWBJxxLqOo/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5377242943756386402" border="0" /><br /></div>Seandainya <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjX1JHGwDztHvTJ8htkL1UYyDaLUMGI72dJXRJR8Dg5mKfE1UDV5eUrbYap5C2T9p7Ye9qa-WUq7F_CQYbsyKQd0RCbqlCv7a9gswsDDUaT4JcL1RNH_OpTE7wHMOUL2N9n4FdCgP1-8DE/s400/23.gif" alt="" id="BLOGGER_PHOTO_ID_5377242930841145426" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmA3IvnwmU5PXSlK0J3Tx7mt9Jznxs4vG1RWXmDOeUBZSbLe8Y78Cw1Ye7BaWlWhbmDmx41aisyt6879hXMjmER4SypheXDNrgDzKm5oHB-y1RFNWCOOP4LIH6hhHK966q3XK-5MWG3Bo/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5377242935926779698" border="0" /><br /></div>Jadi, <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5OTnbRL2uc086mXRXQGDwTpOvdcBYxtTXzJ6x367wQ8r4hMdapKlG2ja9yN4lq9mjsHgMLhHsfzGRJa49cQ0X_0GqO_CYzuZhwxATadxA3B8LDug5wzI6qqx35pdb-FDkDaibmRC_9JI/s400/24.gif" alt="" id="BLOGGER_PHOTO_ID_5377243616260927410" border="0" /></div></div></td></tr><tr><td valign="top">3. <span style="color: rgb(255, 255, 255);">____</span></td><td>Banyaknya akhiran nol dipengaruhi oleh elemen (2 x 5). Namun karena faktor 2 jauh lebih banyak daripada faktor 5, maka kita cukup gunakan 5 sebegai pembatas.<br /><br />Jadi, kita cukup menentukan nilai <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1VHyoBT5xTcnod4WRA-aKQ9v_2-moXpsyvOgjSVKIatZqWIYyAmvN6OWq5holEsc85KFvU-xfEDJSgzRcfHu8BFRSblDNNHZ6GJ0q_F6hGu230Xd0D9ZI7ugHmCb4ZzTmVIf0bR7dq1I/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376101439853705266" border="0" /> terbesar dari pembagian <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNjgGafjXmk9_dVi0hzCrYkR3CFIoodbZILcF_DJ2utlfAQKY94_jpnFNPwNcdR_hBVl7ZoHuyb1eloPDykTV2qq3EgfNCM-VVbsZ_NCS64wOsZcf3pz-jrluI7KC4-oLaHPXiWbSpTgQ/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5377245394006770642" border="0" />.<br /><table width="100%"><tbody><tr><td style="text-align: center;" width="50%"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibTLqasZnAzg26WOJfiwnepGf-Fpj-vGmPAZadNnVZoKEF3-CB0zLzdCo4U82zYix8JjtQxA6LE2eJs8KBSpLaE07LQRToME9H6LmTmU78wYt8YrULS2yXUnY6lKIGOtqN89MsVbaRA6Q/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5377246726559627746" border="0" /></td><td style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipaz420_zXfSUWgLlZDZhcaE1djlN8dRH_H1lLvpqbO_YgSDgmhK_G9SplBXUlreHC8enYY15Pi-uvFixJiqckSXyg1O7LpQdoJutPY50Ph0_6_YKGk6l_NLoHXy5ZllGMGA7L_Wc4qss/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5377246718093017426" border="0" /></td></tr><tr><td style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3ZQe2jeXWH3b8OYTdrfuNfqxRilxNYZRCe20Ve7rk7DmucbDZVW_9j7NDYEhv-WELtY1kQHr-_c9NJI1Z_HH8hXlajpJrWWGEDstJlnbG2VhD8DIkjAEtcq1jW2k8b7bOrQZ8Y9gW_Ao/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5377246713703935618" border="0" /></td><td style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEGUfZeG_irqGqhQZBhMO9s6nEBFIU7jt8JBJTrHMrNovCDONrKQHI0V-c2JS8Mk46xMBivwUkPxkuDlQjC0Nc6Jz-K2uaOu3Fbg6X5EcviOAQdpyAQfZf6NAd616oCMMTbCCW2XqfONk/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5377246639267271954" border="0" /></td></tr><tr><td style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNYTXlmQBcJr0jr6mxo3pQb2AQP-2YGpIlQIIyVZ6JZtJuPHAuX4VxMZ4OPOL2EiCQJWf_TCbhXMMByr1IZgElF8tFNZbBtT2qHRKtEAHzBrS71v7LdzJV_18TLyyEChf38kBR_6mqHBc/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5377246630339589714" border="0" /></td><td style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAy5T6rD_T0Ak7KHqxPGuODP-iDOnNLKb7Kh4bZUnw9ie60VUfIqqrDAJ6RW_8Mbr2z5-NYL5Zw7d2xtab-Vr-NNGGmhPMUz3IgF0vUjUBWIYkeGIPCVjT0kWPPThgteCmr7_ou9aROGE/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5377246622804326562" border="0" /></td></tr></tbody></table><br />Maka, banyaknya akhiran nol pada <img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5jx3Te05GoDT4n-RrVJ_IdVoMjozC91F7BMkRql4e1F6GPCbr7ZcysLZs5d64aLDyNDcy_flARQhuv1g0iXiAj9TWxlCs881mfck86x5hqF62Z12J8utwHfSYLSJGVmR8iexleZIphns/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376100489622355282" border="0" /><br />= total akhiran nol pada pembilang - total akhiran nol pada penyebut<br />= (273 + 174 + 74) - ( 26 + 16 + 7)<br />= <span style="font-weight: bold;">472</span><br /></td></tr></tbody></table><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber:Kumpulan Soal Unik Metematika 1 (Tobi Moektijono)<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com4tag:blogger.com,1999:blog-8125318493233557109.post-92025497707234121322009-08-31T09:01:00.029+07:002009-08-31T19:03:21.579+07:00Teorema WilsonPerhatikan contoh-sontoh soal berikut.<br /><br />Berapakah sisa pembagian dari<br /><div style="text-align: center;">1! dibagi 2<br />2! dibagi 3<br />4! dibagi 5<br />6! dibagi 7<br />10! dibagi 11<br />12! dibagi 13<br />dst..<br /></div>Lalu, apa uniknya jawaban dari soal di atas? Lihat lanjutannya di bawah.<span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPTaTL3zs1_GATWSEKsDiN17gV3Ti2U0kKbtsiA1IylC6WCAWF8S8FCsLCK45gKkdzG81_HcEyWHDC9I0bJ4Ge4nmnzIH07iQKO5xZMCYn5mIw7GFjhyJe-K5Buz8yYXZzFUIcvvYESgY/s1600-h/judul1.jpg"><img style="cursor: pointer; width: 210px; height: 21px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPTaTL3zs1_GATWSEKsDiN17gV3Ti2U0kKbtsiA1IylC6WCAWF8S8FCsLCK45gKkdzG81_HcEyWHDC9I0bJ4Ge4nmnzIH07iQKO5xZMCYn5mIw7GFjhyJe-K5Buz8yYXZzFUIcvvYESgY/s400/judul1.jpg" alt="" id="BLOGGER_PHOTO_ID_5375945662884986674" border="0" /></a><br /></div><br /><div style="text-align: justify;">(Semua jawaban di atas adalah "-1".)<br /><br />Dalam buku yang dipublikasikan tahun 1770, seorang matematikawan Inggris Edward Waring menyatakan bahwa muridnya menemukan bahwa (p-1)!+1 habis dibagi oleh p berapapun p yang merupakan bilangan prima. Namun, tidak ada dari keduanya yang mampu membuktikannya. Tahun 1771, Joseph Lagrange membuktikan teorema ini, yang selanjutnya dikenal sebagai teorema Wilson.<br /></div><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 40px; margin-right: 40px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: center;"><span style="font-weight: bold;">Teorema Wilson</span><br />Jika <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNhQWF8Uik-82r-o_VT2CPHAW8mAnueOC2fW9rUjk7d8QVV8WkM0nyxEGWxjIF-ftoLgJMxh2U4VHGaCrOiEgciZA6DQsDjWagiliGDiku_AH8iqUl-6tVulyA2t2oXBHVPYkflW946Q8/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5375948384391603426" border="0" /> adalah bilangan prima, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrWzm3mRJkRfqKfHAUb0IpBDTaRiaIsyjBkXxfyNBnWp1iJf0KacfCmus4jiXNKzn1boYEKBbcbP8BM-5KGqMr406-o59nGdJ1CZyW5mhKj1HMXokyq3O-RndZrj8cSoQ7VEtQA_EvOHg/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5375948375254044274" border="0" /> <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii_aE3twaDsj-tbW1NUSfSOg74_vGZKnlpsMQ9_p-qOdPpMe1HReB5eDRurbQUYjQ-ASoNscVwLfoyOW86wiUOLybZI9uYQ7bIIBp_LjAMsSbt7HaPiH7AQ94ZQD8Ryfgp3JGmV0q-d3A/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5375948367830403890" border="0" /></div><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaWBMVB5Jdjx5OcF4HRiT14JFRYjf4BvubypJXVV370ZaTcEHqbXV0-_AFAqJTQ_7wI326TDrOe9_CxrsPsKXxm1uuzvi894FQSiJiQZ7hDDMCpyfET_nF7rUJwvp_NIas16IBG0Sbk-I/s1600-h/judul2.jpg"><img style="cursor: pointer; width: 248px; height: 19px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaWBMVB5Jdjx5OcF4HRiT14JFRYjf4BvubypJXVV370ZaTcEHqbXV0-_AFAqJTQ_7wI326TDrOe9_CxrsPsKXxm1uuzvi894FQSiJiQZ7hDDMCpyfET_nF7rUJwvp_NIas16IBG0Sbk-I/s400/judul2.jpg" alt="" id="BLOGGER_PHOTO_ID_5375950200905886546" border="0" /></a><br /></div><div style="text-align: justify;">Tentunya, kita sudah pernah mempelajari invers modulo di post <a href="http://hendrydext.blogspot.com/2009/08/kongruensi-polinomial-dan-hensel-lemma.html">INI</a>. "a adalah invers dari b modulo c" jika <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjADgtRa_hCd0V70vg3Sf6qBCcykPPiphJ1pKwjqX1zmUR3qGPs-asHdYueXRKi4u3GAYyqXxjqAH_xW8tMvnJAQZj-AdE9bYPIzQFzmQThbaBTwdGJBIyl1x39WJ-TrxTRl-yRR_0ErHk/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5375949497765701170" border="0" />. Istilah ini akan kita pakai dalam pembuktian teorema ini.<br /></div><br /><div style="border-style: dotted; border-width: 4px; padding: 5px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Sebelum pembuktian, kita lihat ilustrasi ide di balik pembuktian ini.<br /><br />Tentukan sisa pembagian (7-1)! dibagi 7.<br />(7-1)! = 6! = 1.2.3.4.5.6.<br />Selain 1 dan 6, maka kita akan menyusun pasangan-pasangan yang merupakan invers modulo.<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4xltbzeUEIjbevxU9OmXeNK4-rfcBeRFWpbHnfJdV6XUlsxZYH-81tePSKHEce1kDft1QYl4rNRbV7pqERcU8NGGfqurlsomNDg5qC85nDMqFis8Sm5k6ztwJYjEH3DauTFKl_x99vl8/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5375951602049513234" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnPQk31UOielyi6q1BZq6yhv8MFOfE4TvKtgTcJF6NZai0VQB_Lxgn4g5_QPIIitVdyHxVl7FtpT6H_KZY-37Uohrp53Sl-QuZ7oaxcRqy3KWEQxAJ4BV9SaeqITYpKXp0fK5dPL2gtIk/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5375951593013639666" border="0" /><br />Oleh karenanya, kita lakukan grouping sebagai berikut:<br />6! = 1.(2.4).(3.5).6<br />Jadi, <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjs-TeO3NtnZa1Nh4m0NL6c6mJ0QE45Jr9TtPhqdBBGqAelMawTmhQJyjI_XiYBJs0or-AtxUMcFB4NjL-AcSgc2jzAbkwi8fshMjekpwMEmlsiKSCu9EZSs7jMqynV0GucuuhVWf418JA/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5375957607656781778" border="0" />.<br /><br />Selain mod 7, kalian juga bisa coba misalnya dengan modulo yang lain, misalnya modulo 11.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiy7wrYUZyxVoWpNveQqW_5Jh1lbJxGwbgj7-yP5BV1eBsZNEiV-lz4astX8PyV-gqoUllovb3Z5kjivsNkkwukt-vTAOqSATMo1C6pPCaW6wVCaC0zQxcbIvk5HPEd4nYgpKj2cz1D4ig/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5375959116614881794" border="0" /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXsFXchnNcBDCfpn11M4ULYPiJ-GMVB8OKgfJPIuFv-iu3z7x3-BOOBklgzUn6cCvRTtNDkdvl1JJq6pp_nDE6ZmZN2r5D_QEi2SMxD71OCfC-G-3qM3HhPQablQsZy9a7R7OEurZvOcg/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5375959114463701682" border="0" /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVQaxhaGlke-8TnPI9SkziccM11bYOPYOeJL5gFS8KS8GD_cSmeWtZKTDC7hlwaJmPeygW_BB1ppRn-H-dWiryaPrGK3_XJ0le7-SdjSaNJr_CsR-ehABKH2-QMaeMWEYYLDVtjwFd9dk/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5375959106249575458" border="0" /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKs0AeSDX0o9zQgc-wqtMZi-A2aPiNl_jj9BUEQj3LduRAL0Gd5YKpIrEyuPNSL7GesI3j_nMrphMqs2vCTij9KcFIh0knujyF8KecjdpCyHB-87zg9Fv6Ol4JWJ4KW-dC1crgMGgLEX8/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5375959101868009074" border="0" /><br /></div><br /><span style="font-weight: bold;">BUKTI TEOREMA WILSON:</span><br />Untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg8GWjurfFLYQ11efDCV2em-m4FB0f8wZBYkDDoOY3fMiBvwisQ2dKIktWp5q0wG_6H3Z8PxU8UOxSz66_uR5wJfbg0zWziftG7PHe0sZjKPt8ZuVxzFKJf8TudAWGA6r3uhwUCEOFoN8/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376024788465146706" border="0" />, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe6hPUxJmNdhrIseVV9OxvweoOdXkVNdKXVD8E0GGAX_o1zVZRDoTvC97JVJHzwl1EKIz9u8nmnlamfEQjTHZsPg90heXz8TG-os9if3xlJpgdL9JstupcfGEvFGS2FAK9YcCNmWULZZk/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376024781293693346" border="0" /> adalah benar. Jadi, teorema itu benar untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg8GWjurfFLYQ11efDCV2em-m4FB0f8wZBYkDDoOY3fMiBvwisQ2dKIktWp5q0wG_6H3Z8PxU8UOxSz66_uR5wJfbg0zWziftG7PHe0sZjKPt8ZuVxzFKJf8TudAWGA6r3uhwUCEOFoN8/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376024788465146706" border="0" />.<br /><br />Sekarang, asumsikan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOhNJcwkAPMlwglaAm_pfOH_yaJkkS4QODgJ4kJMsKR9zzzmNiOj0oiKN35n3izXzC3IVAziRiZm2bhl7-8OGwOsy6mv-AXnx8tOrg8L1xOi22j6Sh3RI7S62LNJ8IzT6Wiqc1_NrgJnY/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5376026638925579874" border="0" /> adalah bilangan prima yang lebih besar 2.<br />Dari bilangan 1,2,3,4,5,..., (p-2), (p-1), bilangan yang memiliki invers modulo p terhadap dirinya sendiri HANYA <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxNmH05XRWG_lfbB6DSpUkqDzoWn46tVF_1PRlxhANhszfdjtZ5Zh4mrE9YmRqMtm1H0JWmazxJ-QYnLWpQ7pDptx4auUmSTA3FCBJvbBtNrAgPLTOmq30nzdgvtpCPaadLoRmlA9bSek/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5376027075971930194" border="0" /> dan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3un6NsYkpmyOdHtF0EfhJiSyr0vJUNgXUYR8poPAAlwdpVx3UGsgFJvf5kcOnr3EbXnDQzrf4wK-Fi47bg67MoEQJThADNlbO2k5R0dbwmjdEyyn0oQU33pB0u9UBJAz9KmGbafi3tB8/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5376027067654086130" border="0" />. (Bukti ada di kotak di bawah.)<br /><br /><div style="border-style: dotted; border-width: 2px; padding: 5px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Kita tahu bahwa <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxNmH05XRWG_lfbB6DSpUkqDzoWn46tVF_1PRlxhANhszfdjtZ5Zh4mrE9YmRqMtm1H0JWmazxJ-QYnLWpQ7pDptx4auUmSTA3FCBJvbBtNrAgPLTOmq30nzdgvtpCPaadLoRmlA9bSek/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5376027075971930194" border="0" /> memiliki invers modulo dirinya sendiri, karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGYPZehLE21LG7HYm2xipaBUHX6tQFovXbFzoUMJqKzD6hp6gsFqgBlv6gOJ7w0kibZMZHoQTzY23GdA4-h2o03J3TsDgVjNcEdF55mJ3sOtvStzf6lXaYEBBx9x5xdQn3oE6_o6TeI_Q/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5376027708954085618" border="0" />.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3un6NsYkpmyOdHtF0EfhJiSyr0vJUNgXUYR8poPAAlwdpVx3UGsgFJvf5kcOnr3EbXnDQzrf4wK-Fi47bg67MoEQJThADNlbO2k5R0dbwmjdEyyn0oQU33pB0u9UBJAz9KmGbafi3tB8/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5376027067654086130" border="0" /> memiliki invers modulo dirinya sendiri, karena<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYp5mOJR_dL786yXMa2UVGKjXlOnLog0RVhCfrP4gVUrECE_oMvcxw7H9KdPgF4HshlaOzE7gTAA43Gis1RnhrC2JM9tCka5qV9TTM3K-DaQWqlf41lB1Z8PLYXBE8H53lA4sEyaGkcn8/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5376027697363504354" border="0" />.<br /><br />Lalu bagaimana dengan bilangan selain <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxNmH05XRWG_lfbB6DSpUkqDzoWn46tVF_1PRlxhANhszfdjtZ5Zh4mrE9YmRqMtm1H0JWmazxJ-QYnLWpQ7pDptx4auUmSTA3FCBJvbBtNrAgPLTOmq30nzdgvtpCPaadLoRmlA9bSek/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5376027075971930194" border="0" /> dan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3un6NsYkpmyOdHtF0EfhJiSyr0vJUNgXUYR8poPAAlwdpVx3UGsgFJvf5kcOnr3EbXnDQzrf4wK-Fi47bg67MoEQJThADNlbO2k5R0dbwmjdEyyn0oQU33pB0u9UBJAz9KmGbafi3tB8/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5376027067654086130" border="0" />.<br />Seandainya <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPRzAIdGyTiztG4JwTJ7r3JgQjIGa_LJCKVf-eFdhiOUXRyWtp17jaaxduSW9P10SjNHiXo19BNTdaeO5eRPhXEvoVASafs2J2RSEGvayGhdK1fZKt2XpoHQuvDxAO_SyAbSo-W26kIXI/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376053232827639666" border="0" /> adalah sembarang integer yang mempunyai invers modulo terhadap dirinya sendiri dan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPAxymvC1joFcfdReGr9xtKdyl4LlMQL95Dm6ebhxLbZnPiY6WegHfwXmKDc-tBRCHGPl8Zv0U6g7KPQF3rl5TEI-J4P2cfODe7PRh_y6uuVwkDBV712_0cRvhwvwL4Kqj3ruSgfirgRs/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376053225037413826" border="0" />, maka kondisi ini harus berlaku:<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcCYccTo0zaxlOHoWM1LWeTdIfcqVw2uOyaSFHjC_LCYaWDe1IJ9XwbDvC0D9sspHtS4BBNI5BFPq1VMPyS1o2khDZB4jlgSyYDI5QAHFSDdPOwRoJTItQVtARTMSYIy7NXjJ2JD0T47s/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5376055263549315442" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgelmOofW0zfTExJmo5sbFdpzF-loi9yTNJ1LDTbQDXv2S0cMKDufUdK4R2Ab9-N2vXcv81o-sXyRD1rndS89UKMzQErhKQuLnXK5mkmnDslOsnmpxQs8LLQZKiNMwdqiQODV_nEtOCfPE/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5376055254094954530" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0FlEFXYBdcDSCciXYnmY23PKWYRaa_w0V2DSJKTTwZvB7NKL3PaE0Szm7CaOtR4R6g_OSyYq6CiaM5NQNOkLLrR0i_7ZjjCte025w9SWOVLa7mkSeEUh71CwrVcwJOrhLcf7x2vO1dL8/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5376055253485478018" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcwhtvhkI00p6OKgNhO6sl5B18m5tc5siLyJUZBmwuSziTis3x5w_HSWnqMOPuPr7Pt96Ti7aTzZ4gP1yQG-WfHmJNIdVHJSoTNWU1ginJK6OlnAlcpUVZAxz0AUOUhAy6dAU44PZ9080/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5376055248717577042" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmt52FKPFP_z-hjFA_AeOu6Vhyq_N_Uptp11czlC0CAbox7esTKOhxycC7crVugYidqCIlSztkileysJplnmw3lRGnigC4ekaKC0DkIn5zeyCTk61o5N7aTCwytmIuUvdua9sl_D-PIH0/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5376055239150060210" border="0" /><br /></div>Kondisi ini ternyata berkontradiksi dengan pernyataan awal bahwa <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPAxymvC1joFcfdReGr9xtKdyl4LlMQL95Dm6ebhxLbZnPiY6WegHfwXmKDc-tBRCHGPl8Zv0U6g7KPQF3rl5TEI-J4P2cfODe7PRh_y6uuVwkDBV712_0cRvhwvwL4Kqj3ruSgfirgRs/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376053225037413826" border="0" />. Jadi, bilangan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPRzAIdGyTiztG4JwTJ7r3JgQjIGa_LJCKVf-eFdhiOUXRyWtp17jaaxduSW9P10SjNHiXo19BNTdaeO5eRPhXEvoVASafs2J2RSEGvayGhdK1fZKt2XpoHQuvDxAO_SyAbSo-W26kIXI/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376053232827639666" border="0" /> dalam <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPAxymvC1joFcfdReGr9xtKdyl4LlMQL95Dm6ebhxLbZnPiY6WegHfwXmKDc-tBRCHGPl8Zv0U6g7KPQF3rl5TEI-J4P2cfODe7PRh_y6uuVwkDBV712_0cRvhwvwL4Kqj3ruSgfirgRs/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376053225037413826" border="0" /> selalu mempunyai pasangan invers modulo dengan bilangan yang lainnya.<br /></div><br />Selanjutnya, kita dapat melakukan grouping sbb:<br /><img style="vertical-align: -10pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU2RozuCIKd5E7y9fn692pZTRt1GiwFq3JOIoppoIo_ShtNPm5NXZgvemb_1eHw1TUqogdlRM_6_4JxIfhpf8Fso30L9wTXegRJnZ6iMdKM6YqoOdTUZ2BDsbu4CEyEOoVPOBbLP3q60U/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5376057813068016546" border="0" /><br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -9pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLB2H0LqGVBV_PqbhnYZ6tG-jmE4pJSM7OMLu4BUS2-8a5RPkBxpyTHD8A0QuQcQEJuUX8bUOfH0LLTFIbdwRTcTUX4L9cL6GBfxIcWJAJCy_NDTiEFegFKyiJg4eL_pyVyxghQRWBxXI/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5376058185875893730" border="0" /><br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhF8an34BpB-8bZt7WaHOk_a-iVdwW0MbsJufPUEW7HbDr9AuYy5KiEb6n-7sRJFhKBBzDEWYawNELoWtXGCZgd2NOzO2QwpAKy88M4hJ9Tr8J8wsRLVYfpsiFxPJnA1HZdI7IfbWya2Bw/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5376058176514252562" border="0" /><br />Jadi, teorema Wilson pun TERBUKTI. ■<br /><br />=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir5HW57Y4eNoep8WlVW63vr_FG9dK1-SfcJAPX4qX9Gl0KdB3Uwr9Usn2w6yTj7pITNlwAJpeROUcROpOsNAah5VC2YoqtCQwaUdMGc05ZjVPv7dZGoTrY5KyPwYql6YXLMKaEhn3smec/s1600-h/judul3.jpg"><img style="cursor: pointer; width: 291px; height: 18px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir5HW57Y4eNoep8WlVW63vr_FG9dK1-SfcJAPX4qX9Gl0KdB3Uwr9Usn2w6yTj7pITNlwAJpeROUcROpOsNAah5VC2YoqtCQwaUdMGc05ZjVPv7dZGoTrY5KyPwYql6YXLMKaEhn3smec/s400/judul3.jpg" alt="" id="BLOGGER_PHOTO_ID_5376085448474335298" border="0" /></a><br /></div><br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 40px; margin-right: 40px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: center;"><span style="font-weight: bold;">Konverse Teorema Wilson</span><br />Jika <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJITRSJ2GBCRkoWadgYyDVwyk7S0w58PNT2Xpsv9hczhJyoYQmbTG9hWJkh1ndWDm6A9uXF0dlQOqxBUnXUFU884yEzTJkmeGGlrw1fsGzq0ALaN6YHr2E6vDcnRQSBgbULd5UekTKD_0/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376086053756525426" border="0" />, maka <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjapmbhVAV47TepR-V1ai7_59URs3xiflneWtoALag6eTj8QVCcMgDrN4FYaBu3vMF48o_kkGniEBhOUOcfzLUm5ewgLTyG8jN-wQSsgwVJD3jLvLI9zlJ2EzrfbTMH_fiCXxxqYVoIj34/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376086049703227122" border="0" /> adalah bilangan prima </div><span style="font-weight: bold;">Bukti:</span><br />Andaikan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjapmbhVAV47TepR-V1ai7_59URs3xiflneWtoALag6eTj8QVCcMgDrN4FYaBu3vMF48o_kkGniEBhOUOcfzLUm5ewgLTyG8jN-wQSsgwVJD3jLvLI9zlJ2EzrfbTMH_fiCXxxqYVoIj34/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376086049703227122" border="0" /> adalah bilangan komposit. Artinya akan terdapat bilangan <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQLTOmQVmQ6XdfG8bwR_ZkKj2B4pkFbHnBWsz4KCWLOXYVc7znAOOrMRsUnq8ichEQSTLXBs-Y4G4I0EyQahRT8topoT6Jzhz3GKTJA_DI8oZUXpFY3XFBETDTVHJswLSIlecrD8o0K58/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5376086854709821778" border="0" /> dimana <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaAupvtZEgkKCJKBRhThCr0dRQE6Xuw7m1jTVp8LX8WPZNVeQI62dCma-JWWLAwqrZh60PiNuj3Wr5gxHOWMATSdKHPxeXPJolIOGT7o02omhTdLkKioSkVDS3gLgqsJ21C45qDtPyMMw/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5376086845986345170" border="0" /> sehingga <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLrD7blFXVeAbF_Fh3pSgnEzoVVII1r3QyT8HUqE0vwNHrapvI_xgsCY2HZkTVR250_mvvsTHOKyresenrE9as88gcfAEjGCeGEbPplBU7lQUiT27AreHHwcblzu3oBxVdzPFOAkFbSgA/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5376086842762686210" border="0" />. Artinya, kondisi ini juga berlaku:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfZKO3XUlJwOnXQWn8HO4vVW0vPPwdJejWHiA4o675kgvWDhQogLv4HnGy9wteXqt2zGNkDro1F2zoVMKM2iNbjq5sTkP2slupt3XJfR-5OOGCigP7Pkn_iHuq-iI2Wlv1qsbruwv021A/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5376087285746139106" border="0" /> <span style="color: rgb(255, 255, 255);">_____</span>... (i)<br /></div>Selanjutnya, karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJITRSJ2GBCRkoWadgYyDVwyk7S0w58PNT2Xpsv9hczhJyoYQmbTG9hWJkh1ndWDm6A9uXF0dlQOqxBUnXUFU884yEzTJkmeGGlrw1fsGzq0ALaN6YHr2E6vDcnRQSBgbULd5UekTKD_0/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5376086053756525426" border="0" />, artinya <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLtt3gk1oTg1ly0tsBsChh00vf39nOCxWBa-rFkZvuia4Jw2vRzAJnHVwUpZS6up1mU5dNOoi9LC8A1OOIn5T_7O_yUQBnxLLK8n3xmJVNHUHPQ5vwY35ZJEhG02gpHMcTHT-l2W6OXtM/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5376087871307998978" border="0" />. Karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLrD7blFXVeAbF_Fh3pSgnEzoVVII1r3QyT8HUqE0vwNHrapvI_xgsCY2HZkTVR250_mvvsTHOKyresenrE9as88gcfAEjGCeGEbPplBU7lQUiT27AreHHwcblzu3oBxVdzPFOAkFbSgA/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5376086842762686210" border="0" />, maka<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfxR_hmeKwY1y5XLu8mqZllAvX6Q1DSCp9oOCseK9autYOSagvYHIv6_Ov28_XolWzLc41DTEKuwrxwWb3vIZy688gWrbKSgb3dxrMcKKEV18616DI03D2aeni0fSbw9cZyKzy8903cvU/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5376087865866270994" border="0" /> <span style="color: rgb(255, 255, 255);">_____</span>... (ii)<br /></div>Dari (i) dan (ii) dapat disimpulkan bahwa:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDtJEOl8Qh20o7vALChwYZyx86Rc5ViYU7sk6DaAgIBbozArD5xfrah8dn5cUHiLJGqDFUHwT_qLdV_W9WgXvaeZ6AfJm4r7O5k_mkY0iy6UY4bECqhkf9lT5g-L3ONAeplc3kFc_0PZs/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5376088649958834610" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHK-3czRJ4xCB2jG7MCftra2xysLvqJmtT-kXCl2xAccucTJXLtPyN9XQeXJXn0DWF9phHGJ6HQU4W_oVHwbhgGLB551CqggFdhIdpXmG-ngoFXPbyMVj7v8Mei0nJ2sVpwh0BAAhX19k/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5376088638844528546" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIxv8iV-G7NjrvzgOTN8vvKmHKTBems3t4McHpoElvfPjWP2obhU5j5F7DkQPNYIRCZVYfvVvcUaDKAkzvc8FS0uJ4cbqRx4YqvaSCVQ5MhjD2mpyZCB6jxk5gnYvIQeUPY25a5wodJow/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5376088636809476450" border="0" /><br /></div>Padahal ini kontradiksi dengan pernyataan "<img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaAupvtZEgkKCJKBRhThCr0dRQE6Xuw7m1jTVp8LX8WPZNVeQI62dCma-JWWLAwqrZh60PiNuj3Wr5gxHOWMATSdKHPxeXPJolIOGT7o02omhTdLkKioSkVDS3gLgqsJ21C45qDtPyMMw/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5376086845986345170" border="0" />".<br />Artinya, <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjapmbhVAV47TepR-V1ai7_59URs3xiflneWtoALag6eTj8QVCcMgDrN4FYaBu3vMF48o_kkGniEBhOUOcfzLUm5ewgLTyG8jN-wQSsgwVJD3jLvLI9zlJ2EzrfbTMH_fiCXxxqYVoIj34/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5376086049703227122" border="0" /> haruslah prima.<br />Konverse teorema Wilson TERBUKTI. ■<br /><br /><div style="text-align: justify;">Note: konverse Teorema Wilson jarang digunakan untuk mengetes apakah suatu bilangan merupakan bilangan prima (<span style="font-style: italic;">Primality test</span>), karena operasinya menyulitkan, terlebih untuk bilangan-bilangan besar.<br /></div>=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtpo-JGxYPC2YjomdZlJZUcHW1v-XlSKPKS1awRh3etaWGqGaeY7ZyqWPyX7T824LGiifsM7LU_Zb7vM1A1Z7zoGs7ApAY8_hOJCZeKX_BjUoWF6wLTAxK1YQ1ju1giVruKl_LuUXPsj0/s1600-h/judul4.jpg"><img style="cursor: pointer; width: 99px; height: 18px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtpo-JGxYPC2YjomdZlJZUcHW1v-XlSKPKS1awRh3etaWGqGaeY7ZyqWPyX7T824LGiifsM7LU_Zb7vM1A1Z7zoGs7ApAY8_hOJCZeKX_BjUoWF6wLTAxK1YQ1ju1giVruKl_LuUXPsj0/s400/judul4.jpg" alt="" id="BLOGGER_PHOTO_ID_5376085443265112546" border="0" /></a><br /></div><br /><div style="text-align: justify;">Sekian mengenai topik Teorema Wilson. Menurut saya sendiri, teorema aplikasinya masih kurang, dan jarang sekali keluar dalam soal-soal matematika. Namun, siapa tahu kalian bisa mengembangkan teorema ini menjadi sesuatu yang lebih berguna. :)<br /></div><br /><div style="text-align: justify;">Untuk lebih advance, silakan lihat dan pelajari sumber yang diberikan di bawah. Semoga bermanfaat.<br /></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber:<br /><a href="http://en.wikipedia.org/wiki/Wilson%27s_theorem">http://en.wikipedia.org/wiki/Wilson%27s_theorem<br /></a>Elementary Number Theory ad its Aplication (Kenneth H Rosen)<br /><a href="http://mathworld.wolfram.com/WilsonsTheorem.html">http://mathworld.wolfram.com/WilsonsTheorem.html</a> -- Kalian bisa lihat korolari Teorema Wilson di sini.<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com2tag:blogger.com,1999:blog-8125318493233557109.post-8600266383778854282009-08-28T08:20:00.142+07:002009-09-09T20:37:35.356+07:00Kongruensi Polinomial dan Hensel LemmaKita sudah mempelajari <a href="http://hendrydext.blogspot.com/2009/05/chinese-remainder-theorem_08.html">CRT (Chinese Remainder Theorem)</a> untuk menyelesaikan Kombinasi Kongruensi Linear. Lalu, bagaimana apabila kita menemui kasus yang nonlinear.?? Perhatikan contoh soal di bawah.<br /><blockquote>1. <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3GzQYm-fdYov-uKUgLRuoj2s20Hd7uZt53a0lgitcSOWCijbIYlgpVSEFp_160j-zuZLEK87-M6DC_wzOpvGjSHBe_YZpUXsx5yJ98Ho38MJc1PjY58L_9nLvr0Su0LuJkddtermJQ07w/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374819609989324802" border="0" /> habis dibagi 200. Tentukan bilangan bulat <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> yang mungkin.<br /><br />2. <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX8WL_LhK-0vuLEVYj99jiSp7KA8H33VguUnLeHfHemQIapEQX0h2cXJsu7ZdoZYG0vozMvJ8M5pX8rUXlTJfiunMCD9oqpBj9wb8a29vGuyNHiNfBOVv6qpv3vYIrqgVEYcOtQEZkehLs/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374836206735516114" border="0" /> bersisa 1 jika dibagi 1331. Tentukan bilangan bulat <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> yang mungkin.<br /><br />3. Budi mempunyai sejumlah <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s800/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> koin. <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYXNrtP7VILqRaoYl5n_Ontw2sHkaK_zw8PRUtUpF_6gUDw8tkRbmSVrQP2ZexY-KQEJ3ttbKU_xyS0jorqoeZAYSCCnaK4obJ4JT76vM1L8gVLjWysmwxAwDsuR9xbuhH6rrgO7HmlE4S/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374821797678119506" border="0" /> bersisa 67 jika dibagi 3500. Tentukanlah jumlah koin minimum yang dimiliki Budi.<br /><br />dan masih ada contoh soal lainnya..</blockquote><span class="fullpost"><br />====================================================================<br /><div style="text-align: center;"><img style="vertical-align: -4pt; width: 524px; height: 17px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAs3whicFrDyExgr_B9GFECUPMay6_TDJxaHOQQvnogHtcJymPlHNdZx5o9DDH0H90VlT9_C7y_iIDtqIIuLo0IUhN91ROBRV7jIZT30s2wk7esFtsi0Mxyypes6hnTMqbneiZcWBclh9r/s800/judul1.jpg" alt="" id="BLOGGER_PHOTO_ID_5374823377093651602" border="0" /><br /></div><br /><div style="border-style: dashed; border-width: 2px; padding: 5px; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Sedikit mengulang. Jika kita ingin memecahkan kongruensi linear. Kita dapat menggunakan <a href="http://hendrydext.blogspot.com/2008/09/persamaan-diophantine.html">persamaan linear diophantine</a>. Contohnya, seperti di bawah:<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjBkjrgk6leHbHKItUI_y3o1Lx4px-TzHMiv-h2Ud27AqwFPnE39indhShyphenhyphenwiblSNhn077fRA-T2yVtqgD8T8k6Mg-SSSnz4WKZYu8pec1PIpCuQXInPCHWUaBfopkHDyrzagQx5tNhTy1/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374824587741998210" border="0" /> bersisa 4 jika dibagi 15. Tentukan bilangan bulat <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> yang mungkin.<br /></div>Jawab:<br />Kita dapat menotasikan soal di atas menjadi:<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV-XJh_iLvGrZJ7ZYSAnEl02QTxjkFZiSldMXlzv97fbGfa8L1ofehYeQRXtW3oU-DHciSjogjC6xb9SZQRPHG0NKU7eoK0Mtd3QJQFJ5W2Q88XcsiTDvbBysxr-y7x1yeewXKmF0eeEe2/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374825825447017922" border="0" /><br /><div style="text-align: left;">Diolah sedikit:<br /></div></div><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiy1BYecSjUUqcCca9K3YQiwFdxveryklbTTdhKhkrtOfgDemElwm9Qdai8rxYK0FcJ3PQY3FrUqvukcnD3spMQXffffNTGJVlromHQJFkBO0PQCgYRB7R3FZwUae1x2W5rzUznRveeKgeD/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374826277559589442" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg6GmH7bVzEIbv5xSa3ckz-PKaD0gr3JVMxIUvLs__cpUfwOV6SWKjZuFzGeSS3dYCM9n0UEr0bFBS965G9sUcZ1Fv7SfAQnPXz942ddlqUtTk8vTazyVvGowz2tBaB5_Qb8MInc-dL3LK/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5374826269067246594" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg85fbgX2vR2PIpWAz5f1QGhOmFkUanah2XHtiUnhl_dyphAHjUdlMzltdm24pAKsGBP7-yuYEw8jtoPOeVK1XY_igeJ2l0DroU2s0KqDZy8ivsPq_mX4SaJPovblierkcZSTxImizps-sO/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5374826258680864674" border="0" /><br /></div>Sekarang, masalahnya seperti persamaan linear diophantine, yaitu menemukan nilai <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> dari persamaan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-IunmA8N-vcbVy-26FYlXtBS4rcBGyFeLHBZlG3Nuj8n8YyRSCIYR0hfOM0A1FEuyDjaeRNsO0H_WfSefQddOH69f-4UMuHrBq69VaaJeGTRklEZq83GJdmwfiJ8f4wYpppOYZ1NKRfLC/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5374826855961091042" border="0" />.<br />15 = 2 x 7 +1<br />7 = 1 x 7 + 0.<br />Identitas Bezout-nya adalah:<br /><div style="text-align: center;">1 = 1 x 15 + 2x 7.<br /></div>Kalikan dengan 13, maka hasilnya:<br /><div style="text-align: center;">13 = <span style="font-weight: bold;">13</span> x 15 + <span style="font-weight: bold;">26</span> x 7.<br /></div>Pindah ruas:<br /><div style="text-align: center;"><span style="font-weight: bold;">26</span> x 7 = <span style="font-weight: bold;">-13</span> x 15 + 13.<br /></div>Jadi:<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEgUpIN-oOdyNDQ6HmfM_VaEG7GV_BzvEISUT64LwXJrkz6iAHXO9OGJh4rm-loVaMG2T9uv_vVzEtss5IEaKza-MUvEz6pv-IJ39ihV1c30UL8RBVava6PwJDVfbjR_ZYYM0nrs9nwa2v/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374828960808974306" border="0" /><br /><div style="text-align: justify;"><br />Pada post ini, kita akan sering menjumpai istilah "<span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">invers modulo</span>". Untuk mendapatkan invers modulo dari <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg85fbgX2vR2PIpWAz5f1QGhOmFkUanah2XHtiUnhl_dyphAHjUdlMzltdm24pAKsGBP7-yuYEw8jtoPOeVK1XY_igeJ2l0DroU2s0KqDZy8ivsPq_mX4SaJPovblierkcZSTxImizps-sO/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5374826258680864674" border="0" />, kita cukup mengetahui identitas Bezout-nya, yaitu<br /><div style="text-align: center;">1 = 1 x 15 + <span style="font-weight: bold;">2</span>x <span style="font-weight: bold;">7</span><br /></div>Dapat kita katakan bahwa "2 adalah invers dari 7 modulo 15".<br />Kita juga dapat mengatakan bahwa "7 adalah invers dari 2 modulo 15".<br />Perhatikan juga bahwa invers modulo adalah operasi yang lazim dalam pemindahan ruas.<br /><div style="text-align: center;"><img style="cursor: pointer; width: 131px; height: 21px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYgg_yVnp-P6diC5apacdYfvrNupJQwapDgmKeqnaRzDiz0wKUbYY9f-Rx3bWfgJ2ZKo3d3EO200-YSP-2v2BJyyu8Axoo4IsxsOBAxyWRRt2QYGn1kj4GV-stEoQ2eTeisclIIDuJ3E-P/s400/1.jpg" alt="" id="BLOGGER_PHOTO_ID_5374858220046351010" border="0" /><br /></div></div></div></div><br />Untuk menyelesaikan kongruensi nonlinear, kita dapat gunakan Hensel Lemma.<br /><div style="border-style: double; border-width: 4px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 40px; margin-right: 40px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><div style="text-align: center;"><span style="font-weight: bold;">Hensel Lemma</span><br /></div>Untuk suatu soal <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl7yGtEoCMFwy8omoea9hOZpd9jfF0vSo5aj2PZnDlgqiqIaZqhrGmdFazxpCCWwTqw0RsKQKMsTPlw3BLgOKtsitRvE3Nassh9tulpQzTDkxshB4K_WgSZlfJtm5m-_ngkb4S2L3AKBD8/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374838292450012226" border="0" /><br />dimana <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSpgRyZ80wwZ_QYD_zNbi6iqh9AVe9Mjfh_Q4PC-YViiSHtroWoRYhiP-gOz0wKdHpAni15Q0jBbepfKVY-aSaLP_lx9IYc6WFDzwPs5zO7v2MkFxxlRyev-oCsARBSW_X3JYB1CGXEL_T/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374834829892327090" border="0" /> adalah fungsi polinomial dengan koefisien integer.<br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWNx2DJ0l35aXq-L5ZxcCxAWil56HLWubQOG5u6NQqP6JZcktq0EPEkjNPoORUCoT8v1RjCg3MagA0U1_udn91W1MTaARwVI_nwLPgUxkDaHzj9bYwGsGFz2uGWaNcv3KFU2wSo3DGQ13S/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374833936645316610" border="0" /> adalah bilangan prima.<br /><span style="color: rgb(255, 255, 255);">_______</span><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4A4inAhWwu_L7tA5x6d_1AooBP-BPgP1H9oqalvafLi43EsUWbfbR2xc0ublpXamDzjWXT5dXF3iCHLtWNJgURQlCSqUJw6DlgweGe2bZ6qFTLPoS8ffpIop3FHuvJNGGIl2TxfmGG5eH/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374833930733346786" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1i1-TTv-R8SoykdrPQBYQ4sFXLvIoK2YZIX6unUXYAk59kCyP6wHra-jq_B3h-In3CNUhv8gxaMDFXgjc7QwF-IFv8c4NzS6qXH_x4exo3r-c6CpKPqz10u-pbn5U1Wetra4MYpUQJfGW/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374834834032153362" border="0" /> integer<br />Anggap bahwa <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgz0XPzhGhiSZi3Ut8AdO6YOQkr_L_Gb4tvdqWi145C3T5AjfdOKr3wWxNY4dtNlj-pPsP3sie5mQ1-_dd9S9c0vpXEIRi79wdWv3AVw-umudIMf1JePEjW6oCBmUJWOL1RxDwAKQZ9nk57/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5374838639718511074" border="0" /> adalah solusi dari <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiLiT-d_KgDKZLbIdowaqu9kl9TUOOvCcgeocwLUD46zE0dsTTeAHXuNvCIV2cnO-ILFPYnfRcXwKNCc6dh9abxAoLmAijHe1lRp7cWY_6pzljm01Z1_3f8Y3CvdDknrYp1vYDcXXJgbpQY/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5374838632291367346" border="0" /><br />Maka:<table border="0"><tbody><tr><td valign="top">(i) </td><td>Jika <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqZAkQw5tVIQv638cjfxfGgSd27Im-vvcYL9V5SODFA0X-WFB94iAJkOGCfz6ZNtovd3jk_VsYz6a9DbE7l2nvWvC7gS2tRm4g2hYGJsoxgOpSHydZX1ApXM9PSnZh7xi5_IsQxTeYtjuB/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5374840577421050210" border="0" />, maka akan ada solusi unik integer <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMRXs7OB6Co4KH0B-_disO-xlgPhe9AtzHOr33B1havvLD_OwUurVyMFY5TZxLyssncyn9H1bQyhweCIEDxRE78GpxYsBGCpn7BaeW_gv3Rv0Y3whKmsb0dIdYWIbQHjkAnvTyngy4jUpF/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374840564939334834" border="0" /> dimana <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheuDJKp-kPP94RdI0Ys-haX-EyHf7W3cT000SLet2dQpAn28H00lLxPmwNXHDMEjQAbjZXJfpS9dOrxzSwP_c6tZ-d9B_f7Wxq02SBpnJBvoCH1a8RsxqFnOr9r6JtLnq2Qf0QF9byfLM4/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5374840557172504450" border="0" /> yang memenuhi <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj6CDQPfQo2AJA2HgVSm2lpMOlLoXESe4Oh4YwlYlBZ8JxAelow_CXyW_fdxRGH72WU_4RihHiiQ0FDrj803z7lKb-bgsd0bQErSVQSX695jU4VrdG9I2i5UUHqViASluXkBfp3ALgpDyD/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5374840550189944930" border="0" />.<br />Nilai <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMRXs7OB6Co4KH0B-_disO-xlgPhe9AtzHOr33B1havvLD_OwUurVyMFY5TZxLyssncyn9H1bQyhweCIEDxRE78GpxYsBGCpn7BaeW_gv3Rv0Y3whKmsb0dIdYWIbQHjkAnvTyngy4jUpF/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374840564939334834" border="0" /> dapat dicari dengan cara berikut:<br /><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaowDpO7kCPBi56QaWCfes2OIGAz9PDJta3No0p47SQeASTVLbvL8srp_JQ9okCDr-Qp1RQPNFcOf7mVz36tX1Smuar2wElXQ2T_66V060Z-cGE_FxFdZx1W13_y5uLi8csGtYpyS3IRDr/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5374842393798847698" border="0" /><br />dimana <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixAJfali0fR_m1U10hX0LIlXt2Pqm2lk5pV6GgQOoVppDFFiRpk-uOkIJUL-I7GwgfM7ClvMQ21q6AIrbN7L6tBBI2z8pskiA3BYHnREdJ2z43y6-gjvX-4B1cdCXjWCoWkSeXrZf9kndt/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5374842721691750930" border="0" /> adalah invers dari<img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpqQ1MEkEaCCe9MDtK2PuSgcIXrD5vfz_sWqqxYBjX5aKjCa-ioJ4KQ5lzz5D3G3qIskxHQBr_9khYB7VMDXJ2JN6TQY03KM7yrP8cPIedYrLtEowljo8mC7WVUhld2qS8wNp764sX4vB1/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5374842714702179074" border="0" /> modulo <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWNx2DJ0l35aXq-L5ZxcCxAWil56HLWubQOG5u6NQqP6JZcktq0EPEkjNPoORUCoT8v1RjCg3MagA0U1_udn91W1MTaARwVI_nwLPgUxkDaHzj9bYwGsGFz2uGWaNcv3KFU2wSo3DGQ13S/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374833936645316610" border="0" />.</td></tr><tr><td valign="top">(ii) </td><td>Jika <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWRMz7uZ_oQDx1cPc_t_Hr392wizvLa61hdhREdcrL1-sJMqyXzuNZ3syuu8pSPanbXKR9xturlXS1Nmqkwudglr4FvmlfVmBpFjhYYFmP_6EPqKVDyGZ2p5tpns8VYS3JGl8_YkCWQr6s/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5374850182350242594" border="0" /> DAN <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj664KmPKLeZPOuDdFWiB2b7E28GqwAdRf96bcZEdhUi7AK-DME9ea4lgLlSQP1UkrgF58iqTxQGsApzjdxtUqkjFxvCF2aPP_flU4ueEtluWZ3uGjqR4EmVTaC943_DEz2IOinuwhE8MKH/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5374850171968753490" border="0" />,maka<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ5zwzjrYHW-HAODZZDX7DT7PRXKwuqGwoqQnfwic3rVAB5LDv2jhxdo2AalqNP1ie4aYjy6NRqHsIM_Ts7HYRCzKyEgbFQjWphklWKAOmLHU2ZmHrzA1ruSSLG2ARDnCzPA70xn9JZMib/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5374850164639838018" border="0" /> untuk semua integer<img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMRXs7OB6Co4KH0B-_disO-xlgPhe9AtzHOr33B1havvLD_OwUurVyMFY5TZxLyssncyn9H1bQyhweCIEDxRE78GpxYsBGCpn7BaeW_gv3Rv0Y3whKmsb0dIdYWIbQHjkAnvTyngy4jUpF/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374840564939334834" border="0" />.</td></tr><tr><td valign="top">(iii) </td><td>Jika <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWRMz7uZ_oQDx1cPc_t_Hr392wizvLa61hdhREdcrL1-sJMqyXzuNZ3syuu8pSPanbXKR9xturlXS1Nmqkwudglr4FvmlfVmBpFjhYYFmP_6EPqKVDyGZ2p5tpns8VYS3JGl8_YkCWQr6s/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5374850182350242594" border="0" /> DAN <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDI94Z1tqn30NNgNYxtEeZXla1ItVzsutopZxUsGS3U4_EDn-3r_ybyc0Spjx9Ssn-aWjtIAUnWSjS4flWhHyIHWB_v4_15iruwq3ikOonI55RTWbtTqAOM4WHak-ii13tR87zEwpTLh6t/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5374850155276233922" border="0" />,maka<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl7yGtEoCMFwy8omoea9hOZpd9jfF0vSo5aj2PZnDlgqiqIaZqhrGmdFazxpCCWwTqw0RsKQKMsTPlw3BLgOKtsitRvE3Nassh9tulpQzTDkxshB4K_WgSZlfJtm5m-_ngkb4S2L3AKBD8/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374838292450012226" border="0" /> tidak memiliki solusi untuk <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpI3A-MBvJiX8Z3sKIKx6ooFF87z-i3TB5R_L9YaMb9MfBIqAzHzB1KMSYRuOH9YLeO2suydMXOat1ql_VQhS8u2KmNZA-8YvKE-AKcsekXRWJHYyGlVX99Dj-HzcjsIWt_-fZfYCz9ccD/s400/23.gif" alt="" id="BLOGGER_PHOTO_ID_5374852969270389618" border="0" /></td></tr></tbody></table><br />Note: Lemma ini dapat dibuktikan dengan ekspansi Taylor. Bukti belum dapat disertakan di post ini.<br /></div><br />Untuk memahami cara menyelesaikan kongruensi polinomial, perhatikan semua contoh soal yang ada di bawah:<br /><br /><div style="border-style: solid; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 1:</span><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQdgJKDJPT181FVGWU66efkxWlnDSqA8uBeKvq5hbAhYLrP9aRgE-DUdJeftvgFebQBT3B2JYW0Bx4LEt2a3_y7l2Vk2eCe6f0yTGbO-az1vegXaJWd7Vpf9BRjCmS7m3lqOb8-905FVAq/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374858802720615842" border="0" /> habis dibagi 97. Tentukan bilangan bulat <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> yang memenuhi.<br /><br /><span style="font-weight: bold;">Jawab:</span><br />Soal di atas dapat ditulis ulang menjadi:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwgg0xgx2A9rU9Owx8so7yrPZWbYpg-UvKIRzdmGq7sJHgChyphenhyphenJSwTmPuowkjlGJGpP-hQ45sh6hTMNqmQQbOeRyIiW9E-zl3CUI_JsRlsos0kdDX8dTQdVwLu6EUT-uy22DvdyBBjlLEIA/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374859506164548498" border="0" /><br /></div>Perhatikan bahwa 97 adalah bilangan prima. Hensel Lemma hanya dapat digunakan jika kita ingin mencari <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl7yGtEoCMFwy8omoea9hOZpd9jfF0vSo5aj2PZnDlgqiqIaZqhrGmdFazxpCCWwTqw0RsKQKMsTPlw3BLgOKtsitRvE3Nassh9tulpQzTDkxshB4K_WgSZlfJtm5m-_ngkb4S2L3AKBD8/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374838292450012226" border="0" /> dimana <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj4A4inAhWwu_L7tA5x6d_1AooBP-BPgP1H9oqalvafLi43EsUWbfbR2xc0ublpXamDzjWXT5dXF3iCHLtWNJgURQlCSqUJw6DlgweGe2bZ6qFTLPoS8ffpIop3FHuvJNGGIl2TxfmGG5eH/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374833930733346786" border="0" />. Jadi, di soal ini kita tidak bisa menggunakan Hensel Lemma, karena pangkat primanya 1.<br /><br />Salah satu cara yang dapat dilakukan untuk soal ini adalah dengan coba-coba.<br />Masukkan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixwjqqhOHmWRLRjpK7NWG__hqxI4bi08Wq7mbRN4SRzFq7Bboy4igce-Bq86-h1Ezzw5QRnRlYdecliGVvyPTpJnKsJ7Mk4lXmrvP-i4n1TLwuUhLvhR9xBjulQyG3kE6fUyedT_EOvsID/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374860445876207122" border="0" />, lalu periksa satu semi satu apakah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgCHB27z1LPXaWllKLoElyKF15OMr3ZwBAxFJyh8iF3EvzLotjhmnpCAPmVroN5CY-Ss2YuTedBURF6rjd4fYiYFdgtMajCjXpbRZkyJ6kji2aA2ISiysKXD4l9RvsJgD8-d7Bin2uX-7WS/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374860858882613986" border="0" /> habis dibagi 97. Namun, cara ini sungguh membuat frustasi...<br /><br />Ada cara alternatif.<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwgg0xgx2A9rU9Owx8so7yrPZWbYpg-UvKIRzdmGq7sJHgChyphenhyphenJSwTmPuowkjlGJGpP-hQ45sh6hTMNqmQQbOeRyIiW9E-zl3CUI_JsRlsos0kdDX8dTQdVwLu6EUT-uy22DvdyBBjlLEIA/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374859506164548498" border="0" /><br /></div>dapat dibentuk menjadi<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1tYr3bPQK47-i6Oevm0LBUlCWAzit_ty3xdyRwVNMZGJnVCfS8Mnvg0N7Fr773-RnsednLvy5fN7jWRliOPSBEWhxO-aY1X1qTsOTT-xECTOwbw6_vKI5t1bEb65OC6ItF6GP0zKJJ_Fk/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374882138015078178" border="0" /><br /></div>Jadi, <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYmUGJstDzFqyKwSZr9IxQKnU-TtED1wFm193BtiyZVkK1k9HllFDosN7d7ilTJVf0cocrG4G_oBkHcplJPBP1zjFDaZaswVtMD7az6cmn-uUyGnFAdON3J0cPCkyFDza8i75gaz8ihM1c/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374882276818174802" border="0" />. Karena 97 adalah bilangan prima, maka <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8FZFEdp6FGZqH8-uHqqj3mY9EguizEVgjsFELMdLkiVEc6D3-yHqwoTa7ivw9z8z2KKW2h55_nuM_iECKCGn-U7WxRBSlhk4v6R4-y_fzpNWPm5PfCq9XIx6gZQdd0UNwcPFVten_-0xk/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374882271575609538" border="0" />.<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYKZRmFY2Da8tAcO_a2al1yYdH4DLQylPCy4LrMfg2gFNhoAmn3oNuilPFPmB_VH9pCij4Q3W_0qmqaGJMZFj0u2FAX4fyheV5Z_rU_riAufkhXUFqaZVeKW9Y_wmgHR-qsa49Gi-0nPE4/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374882260910047570" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmKxuthEfw_qABRiX6Ox4W7XU04h0XAeUKNp32oEMczOVOM4l2c117eXPcav36u1lkBxzcD8C6y-YTQ37ZGZSKv5U3PRMqSrDG8ALIwhywpC_zlhyphenhyphenhdH6vuzQhdKI-tiiDujPNeRo8TdvN/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374882253143765282" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiku0RM5SwSMtsNQCyNvSsf4c7UwLN_CUAA_aHhVyV9KVk3ODpg_MixQ-Zi9rx0_UvWOBAfswONi1KlcKB-wpVguWliwCpGF_yuyUk65q0PUElI6BtdiwJfTua9OMsyraBPxFQEhs6DChw0/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374882246597416594" border="0" /><br /></div></div><br /><div style="border-style: ridge; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 2:<br /></span><span>Tentukan solusi kongruensi</span><span style="font-weight: bold;"> </span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7nBJoHqEEq7D6eP9_fwLoGTi1MFw1XOUvprO8_nWYaEejuUZ7DDvt1nPCJMbAbIcKMhkhkRawGsgLfBbdcs3F0UuziF7NeDhvxJnEKsBzZdUfFUaRTLCKlgyqRgWYZW1mmTPAjYQt5_yO/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374884639671792722" border="0" />.<br /><span style="font-weight: bold;">Jawab:<br /></span>Gunakan cara coba-coba. Masukkan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4vMlB3CIS5IQgU3Jr-GV0c9TG-_UPlQtma_ut_VqnRCABiSNli1hXhVw-TIEtCAQ4m4hqXeAXwQHdaGkOLnSCHYur_XDxLTEYZ04SDLSLfciT9TfjsMXI4_VvrFo8zTSTVOeqEcUYaFVI/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374886900700125954" border="0" />. Karena 1 memenuhi dan yang lainnya tidak, maka solusinya adalah <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDTvDzdG6fve2ia-TVYKdf6cCr4hvI1BhVtjaljD5hc_ZlLO2Aj_e06qVd_u-vKLHvZ3Jfs2-iWNSvXekMOQuOiwcBg-rJtQ335_nazPuSo7kQVlW4lXPwmp9dwh4JCDbYlgtkVvuVVR2U/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374888146797503938" border="0" />.</div><br /><div style="border-style: solid; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 3:</span><br /><span>Tentukan solusi kongruensi </span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht9cZnFUXcPa3dRAniEKqZlkw4Yku9sgVYUeh4cKfLrj-arFSEZbVl5FPOw6geIqizHdPoCXJ-x3ysU6negZNTwFf_yGciBE-2KNZMJedEArYONI25Iq8LszvWmRHJ9IeNARZFTIRWTcfd/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374888890715422306" border="0" /><br /><span style="font-weight: bold;"><br />Jawab Cara Biasa (Tanpa Hensel Lemma)</span><br /><div style="text-align: center;">Perhatikan contoh soal 2. Kita sudah menemukan solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7nBJoHqEEq7D6eP9_fwLoGTi1MFw1XOUvprO8_nWYaEejuUZ7DDvt1nPCJMbAbIcKMhkhkRawGsgLfBbdcs3F0UuziF7NeDhvxJnEKsBzZdUfFUaRTLCKlgyqRgWYZW1mmTPAjYQt5_yO/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374884639671792722" border="0" /> yaitu <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDTvDzdG6fve2ia-TVYKdf6cCr4hvI1BhVtjaljD5hc_ZlLO2Aj_e06qVd_u-vKLHvZ3Jfs2-iWNSvXekMOQuOiwcBg-rJtQ335_nazPuSo7kQVlW4lXPwmp9dwh4JCDbYlgtkVvuVVR2U/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374888146797503938" border="0" />.<br /></div>Dapat juga ditulis sebagai<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuD16P64xN3X9-TXFrjD9PmwM6ncw03t50DizIQ6S_JzmL6sVLD0zd7HZKFv36eFy6_1v2_ZPpEBZox7RWoIGBTs3K0kZlyZ-m79Iya6X8mZNMc8ceyia3u_t5TSf0CGpT1P1h5U7ciaYg/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374889731494017218" border="0" /> dimana <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMRXs7OB6Co4KH0B-_disO-xlgPhe9AtzHOr33B1havvLD_OwUurVyMFY5TZxLyssncyn9H1bQyhweCIEDxRE78GpxYsBGCpn7BaeW_gv3Rv0Y3whKmsb0dIdYWIbQHjkAnvTyngy4jUpF/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374840564939334834" border="0" /> semua bilangan bulat..<br /></div><br />Anggap<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7nBJoHqEEq7D6eP9_fwLoGTi1MFw1XOUvprO8_nWYaEejuUZ7DDvt1nPCJMbAbIcKMhkhkRawGsgLfBbdcs3F0UuziF7NeDhvxJnEKsBzZdUfFUaRTLCKlgyqRgWYZW1mmTPAjYQt5_yO/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374884639671792722" border="0" /> adalah (i)<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht9cZnFUXcPa3dRAniEKqZlkw4Yku9sgVYUeh4cKfLrj-arFSEZbVl5FPOw6geIqizHdPoCXJ-x3ysU6negZNTwFf_yGciBE-2KNZMJedEArYONI25Iq8LszvWmRHJ9IeNARZFTIRWTcfd/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374888890715422306" border="0" /> adalah (ii)<br /><br />Secara logika, kita tahu bahwa solusi pada (ii) dimiliki oleh (i). Ini juga dapat diketahui karena<img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMNGhDIbnS3u2v5OnfPV7aCtTZ1y8-jDy51gB-sw3gCTqh9fT0O6ZuCXFJFgpt70bmJnJrTsFDtTQycg7W7N0YbxZFac8uRLRCfWlSfMpMIn_GEBL2uWMiqmPwpO6CKLPo1K4Y3uyMzYVL/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374892090038631554" border="0" />. Jadi, kita dapat menerapkan sifat (i) pada (ii).<br /><br />Substitusikan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuD16P64xN3X9-TXFrjD9PmwM6ncw03t50DizIQ6S_JzmL6sVLD0zd7HZKFv36eFy6_1v2_ZPpEBZox7RWoIGBTs3K0kZlyZ-m79Iya6X8mZNMc8ceyia3u_t5TSf0CGpT1P1h5U7ciaYg/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374889731494017218" border="0" /> ke (ii):<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhz1lYs4Znzny1RlY1Nm4L1FhW5UzHkbFLR2f-oRLHoCC8lb4-DLYPLZyFj38HLK5DB1U50blFTFprnEdbpnAZd8iFolWW6cQoHc9XlBshl8tjk-xO53fmGGTfXwi6vwywBtB6vhYK9Dj_s/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374894651434366018" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXOqHLuu77JWr-eU-1TXKuKJwlAeNjvQPU4QFzzHNpcieY0X0whosNdv1dIuwbpobuAbV8wqj9pa9S9qxfUg1Aopc1npT8QNoYgkOlop-mT1pjSx_tLLDPedYnBOhBDZKtq52lvdYavVht/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374894648960035938" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy_kk1MBweFjIsHTZtDbaVv9xOgRxH4ePhWNzi6_-XS9fBdKGV4t5Dg918FgFt5ZOr5lrXs1iKlS3g6Ho9PmqWfCidklhtSdPYpUX3B2_OHEUzLZbtjohCL6sj44DeHhYcTmVSgfBnUXRh/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374894640133113810" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0i8ch6QKwc7w2pb3hqzYcveIH4etSjONVSD9sdxWEyOIgmlwL_kye9YFLfN4pNp27azmIBORzFnEYQxj8gn7mfrJoNLSMPb_phrkKFqcOlc6B3RLyQeWjfHZsSnNg_y8MCpHUnUG5JgeF/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374894632789564338" border="0" /><br /></div>Berapapun nilai <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMRXs7OB6Co4KH0B-_disO-xlgPhe9AtzHOr33B1havvLD_OwUurVyMFY5TZxLyssncyn9H1bQyhweCIEDxRE78GpxYsBGCpn7BaeW_gv3Rv0Y3whKmsb0dIdYWIbQHjkAnvTyngy4jUpF/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374840564939334834" border="0" />, <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZsLFy9UZYOOlndjWxhjCK6iRyvV37c7yCzl5DeLdW2Eux4I6HRalBBHvOEVnMpSSTWjnAI0KhYD0n671PKJVVWrb_a07ozkzSfNPzUib34R2F3AzbixDjhwG-rl0U5XEwreuUckbEIAWd/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374895770313967202" border="0" /> dan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlpylAmFJ-HWFpTIXtHfcZVvUF65ef-AEdpBnde0mC871ezfqVslw4fyH-eDaH4FxR43qoKUEakeiTekytsAEkrl3vfLF5h6fKAX1cxf_aTw1lwj2ya-zCJILft1U1IzcYcry98LhTfTYx/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5374895766167352530" border="0" /> selalu habis dibagi 25. Oleh karenanya dapat kita tiadakan.<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7tNxAFBs_xjqUhZ8G64cKWcaMPYIFBWZEqINXba8uE7Ncpp99v118HVF0oltUhRriExQ5_kbHTbER8H4eHs0__8Xvd5_fWWvHilWkhSUVdLHS60_M1kFyoYM4JvRl9wZ6Q3p_HQODPFeM/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374894623035013266" border="0" /><br /></div>Kita menemui kasus linear..<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKWK_WtqqsVLgpMfOdIgoEeNfUUN1J_MeataW98AtEYecR5V9ihDAwieLNrLumwER-KnmkpFrsKiVoMAo8ADm2dSisfrrlUV6Bmm6NVOAjZyEt35-Sbjop3Xu3UZjPLOTrE8Z6A-mBJrGr/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374894481327396498" border="0" /><br /><div style="text-align: left;">Bagi kedua ruas dengan 5. (Lihat <a href="http://hendrydext.blogspot.com/2008/08/modulo.html">INI</a> pada pembagian kedua ruas)<br /><div style="text-align: center;"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3out194ykB5zMED5Bg8P9d5LRRkd6Dqr7R15bi-mYuiFIo5wkRgRDI_3Sx5KBofOQnIQ9GpIy7IDjbPIc8-MvRlFxhsOwpoWK8e4QBdADXWxiYitO5ih-rIupLHXJGZ4CvfGEoD8sMX4/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5379461075269723378" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVcN8LQeoaK2Gvdvx76Nkwb7dKV_Gkmk8Edt48enJUjnKDK6bY7IB0Pa0nsCE4uxF7SdjLt8zmfBQ3d6TsegTCESz9v4wgfcHYZSEMHQUHSi6l55qIemgOZyxnTI41Q23mpQZ4hzc_3kw/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5379461067071065698" border="0" /><br /></div></div><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgatbZpCurkxM0vBoDbGIebymKswqHACLVhvMM100k2Wh1cPuoB29wsinS-IWhNz0SrchRhXMDYh0gBcUIF1YGg22YdS_rfaEFyYMDL1MGFVLcbvg5m1ZZpv9IgGSyTKxHrBguo3sTsIoKA/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374894477335826642" border="0" /><br /><div style="text-align: left;">13<img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMRXs7OB6Co4KH0B-_disO-xlgPhe9AtzHOr33B1havvLD_OwUurVyMFY5TZxLyssncyn9H1bQyhweCIEDxRE78GpxYsBGCpn7BaeW_gv3Rv0Y3whKmsb0dIdYWIbQHjkAnvTyngy4jUpF/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374840564939334834" border="0" /> dapat disederhanakan dengan modulo 5.<br /></div><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZxNnrL5rwbRuSvE4XSN5s8AEDgi-r8gp9jn0_1Yr_f0YYAqPA674rN2rHdIhFbtKtYdqSPq_vV8Q2Xx57lJhdfFmCN2xUuLYGQIGmUhr4SUjZ9_LASnpAQMD_5oPEFM9-dK5AbUSrNPA2/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5374894468960062466" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2APnXXe5flnlW14IuN0i-5z0OsvRnyhkGgp5gCjxrontcc33Hgs0GbYNr7a03mSH3qbczlLJgdmqe2U1KcsyvrvOjL4fLiU5ksOW6A2oqvP2k667wnYiK9xZl_3U5GWpe8a26d10FybaM/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5374894458951694962" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSmjONHP7rr_xmc-7qd8LCYoC9Ik6vd8KrejHkqmSDIFzCHSg09PDiq6dW6tGtRGNJn_SdlMxwlaimqDCQEHRMbpy_lKqc9ga5Gx2BnGWNtimBhBWpOklPhKkljCQvRg-FqGMNSeL75Qhyphenhyphen/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5374894451005349682" border="0" /><br /></div><br />Maka kita dapatkan solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht9cZnFUXcPa3dRAniEKqZlkw4Yku9sgVYUeh4cKfLrj-arFSEZbVl5FPOw6geIqizHdPoCXJ-x3ysU6negZNTwFf_yGciBE-2KNZMJedEArYONI25Iq8LszvWmRHJ9IeNARZFTIRWTcfd/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374888890715422306" border="0" />, yaitu:<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiuD16P64xN3X9-TXFrjD9PmwM6ncw03t50DizIQ6S_JzmL6sVLD0zd7HZKFv36eFy6_1v2_ZPpEBZox7RWoIGBTs3K0kZlyZ-m79Iya6X8mZNMc8ceyia3u_t5TSf0CGpT1P1h5U7ciaYg/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374889731494017218" border="0" /> = <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEge6t8i6zM1hmlYA8qWuZ5OTrT7z3YTZTOiSKFOjOC_iGKcecg-z0QRial2kYOMlmpvx4CIRWKN1eXOrrPj5EPI3S04g0p8lGiSPRHrOSfPrelcghemHqZqqOnB56yuFM_kR1zcnFWVRRVk/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5374896922230396882" border="0" /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj4EcuXbGt7PYcVUaWaEGwpfHMAWPEjji_Xq0YxKo9wZjTchlsRz4iVBl0NG3bQ4YxUSc7VKYMLbMxvl7h9zGpmvskbFUJ7-f21UUiJZlOZ6hV65e-3QqWRhPYD538htcGLXWL5pU8q07c/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5374896913642202018" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb3XfodxnZ3PEn46no4-x5g1gHl1mb5eFY26aDqB2BgZUmNzltVnS7GWyrpovpbAYVPIbiQPfJkQnjzXBK16qDW8m28UVjohuBhfOQl1lJP_BTnrI16ofZwtFmn-aTLnT48lM3Fa7tyhXi/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5374896903794600546" border="0" /><br /></div><br /><span style="font-weight: bold;">Jawab dengan Hensel Lemma</span><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwcziWPCP0RgKsgIs7Axbqyh5uoCQz3RPwT8urO4o18g7rEOkKxxsTCCApGoGZK-c2Fx-GGbO5JI9PFsQBgVSQxXk0tJX6rhCN3VsH1RXPcP53DdSOTqozN2SevPdl2i0otYXItAjQRdPf/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374897705584915298" border="0" />.<br />Solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLAIuTiZC8MqDktPFl4dKOQNWPPoU7UYtrP_10ofke52DSnzM90HP88qoBwUzZ5IGx7LLvb41p5fkkwKDQDoPo0rTxC-rteP8itdvkQzZHl2nBZOIjwaouFpQGM9Z4cX4BKv16QXR5USFP/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374898311921801138" border="0" /> adalah <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDTvDzdG6fve2ia-TVYKdf6cCr4hvI1BhVtjaljD5hc_ZlLO2Aj_e06qVd_u-vKLHvZ3Jfs2-iWNSvXekMOQuOiwcBg-rJtQ335_nazPuSo7kQVlW4lXPwmp9dwh4JCDbYlgtkVvuVVR2U/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374888146797503938" border="0" />.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfSkX6TQpIOZI3dzxr5Awj1hLfmYgyNAQxvNzixBWh0o1JZiZMlMtIiDuMtf_0POKSffWkxwmIBYN3pwR-Jjt23-Q7xIUiUP_JCKVv8tiPgDCvhGUxZZtlBF7jTX-cJiJ5rcf4DGREba2A/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374898904520981250" border="0" />.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrfRSVaBvYrNhVIEVC75G3USR4Ew5xobSzY5j9V70i3cXJSGZU8nHWLXJHT3pLRVa8ehRmUoMQeUWKLK7oefeHtEO7A2rd58-SzV75RieK7K3TbcOfJJW1zuCq9_4-QYn7_L-2Mf5MQ2Tx/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374899353491542418" border="0" />.<br />Karena bukan 0, kita menemui <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidss5mNlkSY5iTH7zAJjMLzshVnDSBM-YewEqWTXlh5xfHyAGeml_SlGrNT5HjDiC9SWJO5Z1wylWqkIiADx2BTWeuIrURxvQB8XQFV-X1I2vH3uPkkxHGV5xUQvqv_O4JZF1nOnxZS0RU/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374900899048030002" border="0" /> karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0O1QCvCODV53Z2oHEUAsr-gxUzuoPyiTVFuHwHqGqd5SQ_H8L1MwvDUEDCziaVlyjTBNdeJNlqQqYxFI-LXJu5J4XmepdFaJYaDZWPscMAwC1fiszjO_5eKvjjZYtx_GItKExt_SL03nt/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374900888963002066" border="0" /> yang berarti 2 adalah invers dari 3 modulo 5.<br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizpFEhVuZaLxdTWL_zYacpsN0aBq9S-nOZ5f1zSQbzPRvgyDruesZSnLnTO4FwY1ShcesdCGiBcAtssvXIKfhIQQKqYVy5rviElqiln_oZyZIe8IS4EukyzARXnenpaYCyRjfjb81kO4sK/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374901871525787314" border="0" /> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVpbbtfMTh7IZ6BAhXh__rKlhSBerwh9X7Myg42LE-71LS0qhG5FpHdo0cqW6YwtT12MPlIMuJ1CwvHd7zQ3qzCcCh2o5oSSTPq7x25LA3EjMXulAHA_AqvrrUXHvgmrz9YITZCPZLDQ2f/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374902189376386930" border="0" /><br />Jadi, solusinya adalah<br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSrUrPqDXRJJH-5dg-qaH7yd87Yb2WXzK_QQDcazUYdSdBPewrQcvbXFPHWWrhNTl-Gpc-RYHai2y-t7DmSHIHvs7JidQIqAQfX2qZ-HdERZTqkS_tRBe0u52vqraWRkJgf9GYfqdwfUNk/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374902925682274114" border="0" />.<br /></div><br /><div style="border-style: ridge; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 4:<br /></span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3GzQYm-fdYov-uKUgLRuoj2s20Hd7uZt53a0lgitcSOWCijbIYlgpVSEFp_160j-zuZLEK87-M6DC_wzOpvGjSHBe_YZpUXsx5yJ98Ho38MJc1PjY58L_9nLvr0Su0LuJkddtermJQ07w/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374819609989324802" border="0" /> habis dibagi 200. Tentukan bilangan bulat <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> yang mungkin.<br /><span style="font-weight: bold;">Jawab:<br /></span><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNKHvl7H0b3AThbJZW4QHOOzwSxgFExQ9oDNczI_4mFBoK04AoDwr9P9KGG8gTQD08_8JPy2NJ4rO4I2T4eagB7nd26MORd69ArPExqQ1HYCsz_pD9IpgAU6JMBOw4rOp5HwonFYuWl7kQ/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374903858581931938" border="0" /><br /></div>Karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh40CiY5ZUG4HS63NERzrFXbqadzP2GvvUmWFyC62lGZdWICyuSHJzcZvP3qhs0rCdHq_mfmPk_QFiBld7l0NzOplZJ849YxX9vb95OBL0y68hEYJo2ejj2jCEEE-LPtszCrdePCIVPietJ/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374904222537987250" border="0" />, maka kongruensi di atas dapat dipecah menjadi 2, yaitu:<br /><br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYfHDU48mEnGBc6CP4ZmyDbIkILUUdodEC9QUQ9clM8_k26cva0XJUIXcbAP3mMKw3vEz2D5qSqS_bCALK81Xyw0PTWlprF309p1CVvxjdJaXTYFvXJVW6WpKsoCe18iOKW2sLgNee5IMo/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374903853770371394" border="0" /> ... (i)<br />DAN<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht9cZnFUXcPa3dRAniEKqZlkw4Yku9sgVYUeh4cKfLrj-arFSEZbVl5FPOw6geIqizHdPoCXJ-x3ysU6negZNTwFf_yGciBE-2KNZMJedEArYONI25Iq8LszvWmRHJ9IeNARZFTIRWTcfd/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374888890715422306" border="0" /> ... (ii)<br /></div><br />Solusi untuk (i) dapat diperoleh dengan coba-coba, mulai dari <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqfAQZZTvoxE7OjrYLFraXn-HlYIdFiQvpc9SsU7Ij7VvGsjgYBrjU0VVR3LjRmWneeEbXTr20xguLrS6p-HyfUYCooetXo2qNZLW6J4tDzn4LehSfc14Ix2yHDjSN3lMYCfycpRytnfgw/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374905029474782210" border="0" />. Kita dapatkan<img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8snza5PKnp1DQ7mFiEQFWXNOBpYonFU4DAw1rjWO1aTQiv-bRNSMX_HHsaO9FWOxKH_7hGQ3lWqfjPOr0YgUNE684jvo_1GlIQUjO-PjDhyphenhyphenjDMBrR4vQhvK-AstM6GWZXgsP6_kZZUj2j/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374905022646419458" border="0" /><br /><br />Solusi untuk (ii) sudah didapat dari contoh soal 3, yaitu <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb3XfodxnZ3PEn46no4-x5g1gHl1mb5eFY26aDqB2BgZUmNzltVnS7GWyrpovpbAYVPIbiQPfJkQnjzXBK16qDW8m28UVjohuBhfOQl1lJP_BTnrI16ofZwtFmn-aTLnT48lM3Fa7tyhXi/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5374896903794600546" border="0" />.<br /><br />Selanjutnya, kita dapat menggunakan <a href="http://hendrydext.blogspot.com/2009/05/chinese-remainder-theorem_08.html">CRT (Chinese Remainder Theorem)</a> untuk menemukan solusi dari keduanya.<br />(i) <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8snza5PKnp1DQ7mFiEQFWXNOBpYonFU4DAw1rjWO1aTQiv-bRNSMX_HHsaO9FWOxKH_7hGQ3lWqfjPOr0YgUNE684jvo_1GlIQUjO-PjDhyphenhyphenjDMBrR4vQhvK-AstM6GWZXgsP6_kZZUj2j/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374905022646419458" border="0" />, maka <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJxSpbSBkJ-6F_9bRlpMEs1uQlqoD4a__6cgaM0cEZpRCB6PgnGEAqCCo9qAqz-UXD_3kA7hiM8gXhaYoYEJFXya_O8nx4skgXhW4GOfLvmD_W9zFBl0uECJM_0aZBqIBooSsuVjjc6ll-/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374911723793856562" border="0" /> ...(i)<br />(ii) <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb3XfodxnZ3PEn46no4-x5g1gHl1mb5eFY26aDqB2BgZUmNzltVnS7GWyrpovpbAYVPIbiQPfJkQnjzXBK16qDW8m28UVjohuBhfOQl1lJP_BTnrI16ofZwtFmn-aTLnT48lM3Fa7tyhXi/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5374896903794600546" border="0" />, maka<img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhoRzFI1XNakAnVhwvBzCQhMdT0yD32pSEaAtMkHYue8bIXfOFy5kCjqYBUnLOKKElHw1KKPhauyWGGPdl5IbvQuih0Y79F2EByD2nPTYjcglyO92yghCxOfxe3RXovksaX8Np6-168xy5W/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374911711327420978" border="0" /> ... (ii)<br /><br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWbvsiwruYQgFhiykjyLtfsA0eh5c9Xej3_ugIuE1dXkgOltOe0VFEe8Ny5lwQd6-5Zf3N4v4YpK_aknVrchAYQ08uItRSpmvnRE7bn897zLRg2bxS9dtxOHBhWlpkYpggAjA-JUlRKE_I/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374911706886467266" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJKjMlIyCbwyzm8ofVWL5R1oGsIlCvGTm3TCF2Yw_qzxQiq7wItXm3pxL4qFc7biW-5a_t7SDRbdMesCnhmOnkFYa2n3W2vi_q37VEcVUUxFHxjwJ8Kl7EffXt7eZBY-5Bh0Q65ZR_Buwu/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374911582826585298" border="0" /><br /></div>Kita cari identitas Bezoutnya dengan algoritma Euclid.<br />25 = 8x3+1.<br />Identitas Bezout: 1 = 25 +(<span style="font-weight: bold;">8</span>)(<span style="font-weight: bold;">-3</span>)<br />Berarti (-3) adalah invers dari 8 modulo 25.<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqAS_ABILbC9lP9GHlxgB5emg-oRFR4ktdrQAKQAaSbhwosVTNI65Rsj270ekxnZNeRktdhHZ5LmVK4ygS4WLywZRgKRcy6zgBfyrdV2BDwLjtlZpMuHfv0LPclyLaNvTDx-tD9ukyThZn/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374911576410683250" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-mTholQPL2bq3tIKTqAxjFlY7r0ByRyVE-w5MKpPAZVLGg4SWeG2zDb6XRBr3C3bGfzYZLMzpIGxdeWOakDf6YAewykxav7M5LlYnVGAqSzsERz_Ug5ZNSXBgsIseruxFsHku_OQJ-Unz/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374911572220775554" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9CyKApmFFGkTc0C0Zu2YZ8-qUm72pzO-yKmILcapLcxvXfba7x1CNWBWzk3QIKMpW2Df53zCxFG2YEjaPvwtRvmEAQ9zoRmkxCJtj_qwm3UiuzburWkS2KVfLDHsVOeLdKZl9fmLhmxM7/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374911560157001138" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaCekX2HNwdQ2bDChmbQJL6BbHr5U5gXmrfzeZciCWvDgJ50LNpMbTUA-3J1QQBAE0Dc-_6PA49rNHjmcTgWelYUd0a3vUvN2bb208c-BpDQnCl_iPkMKPWelrWmu47-FeoitmSFLeRDPj/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5374911552993395234" border="0" /><br /></div>Substitusikan nilai k ke nilai awal <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s800/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" />.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixsuTJVJIf_17zq6OD3thYdjUujWTm-LHKM0ovmYMnKza3FfN2OqLtTOximvo7MKFy2tT7_B4m2t2Paf2Dara8vuxbgGNnmlJSmzz9hsrvBfl50gybVfLq6Bo48UKjsuY6HMjuvYxZaYG0/s800/9.gif" alt="" id="BLOGGER_PHOTO_ID_5374913434596196914" border="0" />.<br /></div><br /><div style="border-style: solid; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 5:</span><br />Tentukan solusi kongruensi <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnN3X83QVJL3W32DID2IadAgIJ-6QZdt6lVhXvUT2l0Eo_PR-OX78276pHZI5u9LNJ3XR79JcgY7HWBTS44eNLiqt-U2WH6RE_w4WEdNY5JFomOIrHDw4GyOk2b0-Y6EySJSSNPmqX92B8/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5374917627217361474" border="0" /><br /><span style="font-weight: bold;"><br />Jawab dengan Hensel Lemma:</span><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgaBs_X0ABMu6-B7cBogfFtbnDYDwuixdMykVJcE_9_vIwt-wDN9AEj0S2SNI5DSjiwwhj_sCUbEBAg-IUFK15R-3XI677P70rjJNhpLzSiYXKqHW6l7RnuO9JmBcvs5tNdx66AeDBnd4LG/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374921558183350978" border="0" /><br />Sebelumnya cari dulu solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6LGl-C9RgY7puY9HsChn8-Ck_gF_25HGxJw3TVsHcSK-fjvY_kGuDKhdSV_X6350VRPD-3hsp4NyhtTyx-9Ub45OuLA2U7MYEZWaHDTg3uaKiN5IFfb3iUBMvwmJs5bprjMkJaGbauIC3/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5374917840181996098" border="0" />.<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhg42qw9lK3HlIMTdTagMA_sy3lev5PBZEuA7f9aN2epzYYSFLc8zcH673vmX_mrsLp2gGjWP9RGRSov895RFeIDqfXV65wTusfAYezF1pv8ix22I7SsEbFmRYTBqyXeIHjWjI5QWhfv0WL/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5374920101455038018" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZGX3z6nwd9WzW_vuGrcrJ2BjiSPCm8dqMwzQk22xQFWnAeVhv_HrNB6s19nhpbqbwKPyW9oBK5VpD3CW6Z3nAsOVg4xsWceeSQg31sz4Ysos1tZT8z13eZDLMG0LjBVmwBJq1ZpQJkOJw/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5374920090590321730" border="0" /><br /></div>Dengan cara coba-coba, kita dapatkan solusi:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7-P6-qewpntMHPGmpFdAxJT8Hk5wYvfiGj3LJt8H2JGRWhN7JLbHT70fq5FtuZJy2XXVlQP8CKZBvRUe9Taw4MnjShri2-GkVrwtdMbwMmouAtskDz0S9115gQl6OEoDl3xjcKf4VXjC0/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5374920089312860226" border="0" /><br /></div><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjD4y9EtaHADWgWQ6E3DZNH0VkRtme5_8EHh45UKceBZON7fKAwsZupI6NHExKrWU4mHBfgi8OIE1-lykRInH89fzlfvoXZP70TNf8En5PXgibgHqcDgYGiKjdKAaNVFGLR62bUCF58JiPf/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374923202651371314" border="0" /><br /><br />*) Untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgalJHsdGYECimZ0VkOEEjQP3-CyJ7JRzgKRerlXC2BYiWIYnW2qKpvvyWwuyX4y2B9nwFczE8wwjPw10u3i0L-MU2SbAcoyNAkE8Ccpy1iXKNUnWDvf3-k3Cx6hFMUiq668WihA4KkIPxL/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374920740868174450" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaeMW0-6rpiJytIeF2UJYL2VNOkctPZSO_BFWQHD1A5nYGtKOmY_ltGi29yqbltVqfYh5qVbhqGkTqCUgWSFhzFe8ydX8LQYA4_fNS7bXQWo8c_aEcpzuiL8oNP_yrIr4a4YKv-Pe0f2rV/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374931997752790274" border="0" />.<br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgluL8a4H8o-EUxzF-_ZnrQlxTeLaEtbyfCWI6eMx4dPSWvCLs77ZEjzC0pfbSS9A6HdgE18_wVxuoecHBbsgpSEWzcy3GiI2M9jxDydBmswvkU_4BfKML3ppiP0xf1t1iwPiaBz1pQPlKU/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374933862074197282" border="0" />, karena 4 adalah invers dari 3 modulo 11. Atau bisa ditulis <span style="font-weight: bold;">3</span>x<span style="font-weight: bold;">4</span> = 1 mod 11.<br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSnlmAYIwiOMksLUI3sLdjdSamuKqbmRCKtmUkpY1rToW4iHoPsteOU8y3vKhI6H8_vaNB9_k7Q6V0ocrYTgTf3hWdNTuK2DjxVZaD7hxRPiLaMnmqYhNc95VcMrUVIHxCipOxbUGZuD-E/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374934991570884226" border="0" /><br />Maka, solusinya adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiZIyyQvHxCHwhuHjYibccQVZQY5ZdpsD1IA7OPEYt7tzbZ4kQdNVdFL8eJcTcDyrzPaC_G-6UobeDJUNmZ4ZQorzWaJ1INbwc35hxUOTORKrNI3-G1tW60BYw_EfZmabzOG9epK8mk_jZ/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374935691733965522" border="0" /><br /><br />*) Untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUj36tlSbedGWud79VABdH6GPcwgn7cK3PltgpqwXHg1jnA-x6iFJ8rDloizmBodX_vCVKrrwsxh4ocIMJ4eCD34gc0S8p0Kv7NOlkyxmmJavod3G5NPQscXkLUjlQls5ZIYku6MPbH_zU/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374921001564429842" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgr3l6Z0meubHX7prvuzpk10ZsDs32qdJHwEdRxjNzoq2pqVxRNwp2roF84RTrOveHShW_Yq2XD8T5eqAqbQ8LHCMF6G2IbZgn0stV5GzHHlsfloIMADeXtwLyWQJeyD1vyp3J2y76EKRJW/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374936132319920002" border="0" />.<br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhne65-V3upCYLxzi9iyngdg5yvEwM6j5PAyC76-DEOmmI06JyNfDTwBHYk2HzMTBjjM7Gk7T8T3vnmc3eTcnygu21ZjpBmjWXOHsSmJopplNwc4-ZghH7SPiRYT8euyjb7z1_wVUP_DTtY/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374936821883787506" border="0" />, karena 1 adalah invers dari 1 modulo 11. Atau bisa ditulis <span style="font-weight: bold;">1</span>x<span style="font-weight: bold;">1</span> = 1 mod 11.<br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoARCpoM2hfMnuZkmQk3Zk49LA6rBTuzu4iGpEYa_CrCax3Duy-V37QNuQ_0acsKZF_raZ1bCjx3Kh6z6Jz5S_KgkMxsBem_LhonI_XOUBs1DPPY0evqGzGn6DQcLP6swfJucHz1_2qtVx/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374937629733268210" border="0" />.<br />Maka, solusinya adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9p2HHcWjri6C3FBL_mayumqMqdUURMosYwfam8DVIAgFbmElX2t427sT5EsYcV0OI3NqdQ7nKYWwreHn8ua6-MpJiMEeE6GJC-N9mL_cnzGQvwOHD2ve8BDlMQsBV3gu8wD-FGV7n340q/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374938304632883506" border="0" /><br /><br />*) Untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjUfbU-JHf9LSr0yzUx6W5O2lJFXjQNyyThf3pP7yccQqbIL_bDYZwhzHW_3mGSZNY05GHQdRB-v5Yrw1IJJXJ7ORO68gBOTltpFQMY83WBLE_-RgyJJ0G3iIlhEcGB565xBJoxC8ZSFrd8/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374920993258672114" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihGTFqg5y6osRLw6idRBwGBdYQqQk-SXJCcDMynZ4r2ItbU-3dYfbMzsvAKvR_zsdXLqZKcWmdaQxymM_G6Z7rRfoNh8iqjqVlNrf64qxqi_tvi0d-ctxuE5lP06KrDOZ-WCE3mfW0KGw0/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374938794128979586" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhwUIlhXnoSx7r1cLHK3q63DJamyW7_Loa2qhIYI5mZijN1RYqZLp-oWbXAkz69vK2z10Lvq67soKnk-xLV8RZnkpphIaAHyHE3quIFSuygOE7kdst7KS0MdQe9TqyfviAAjd06zo58PjG/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374939297235732546" border="0" />, karena 6 adalah invers dari 2 modulo 11. Atau bisa ditulis 2x6 = 1 mod 11.<br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbGpCoUBcghdcSTKhpSah67np5unqtMqzCA8rVRpH16cXD6JIDc825tI_qnnhkDoeRsv9Vw7F5LxQfdJVe1raKM8FLMZmqfkXOtyNitK2-eBZlFrcRlFIwLTjkGuDQ0I1TDFub2RR6lgej/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374940739327959650" border="0" /><br />Maka, solusinya adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHyL_cDkTfDMqHqwrJz4zEhud4_sWCEul-X5U67C_jmDIQrfYAZqhYTQa3KeFbq6_ovO2rOHPdsfY4ujdYjiC4B3AAecXQ7rO9o5AzRAZ1qKHvuvdVvh2ERO_rDNKXtKQcFdvDoVdJZ6Kg/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5374941405826068338" border="0" />.<br /><br />Jadi, solusi gabungan dari ketiganya:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfq-NYRiA61v6RZSHcHylB5y_Bo04q5HQ75jK70NcOU2TyyegL6tUg-n28OnAOZ-yrUu1OLYmdDn0VkSCX-ASmMMGvJwYmB8USQB0N61ntw7QaJ-R-Q2kerVWYhXRht5V8-jHuHVbsldlb/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5374941820002673730" border="0" /><br /></div></div><br /><div style="border-style: ridge; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 6:<br /></span>Tentukan solusi kongruensi <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMFF1NWswjQo502pf-lj1_3veESKIKg0elm5sGBfUhARvWdJoggJj2i81Ursc4mG8tNS-Q8TV2K-QXzLexFktjCTqW-BjUOL7BMt0T4zkNjMeFbNl-TRGmyi1CXh7ykrAdbaXvjON7hmmB/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374944891437074482" border="0" /><br /><br /><span style="font-weight: bold;">Jawab:<br /></span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyFF0vYFOdE1f9C5QWZQ8iU8NWSWq8e3jv4eYcYazbMbqgOwIb6hgP5GOR473RI4igt1To5XhFBhSzUoyS9aoXxKZcjCy_hfltqgB8UszrcOqN0P8lAmRa4rk7qh0Xgs1QsslQVUuZ60Au/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374945369684743762" border="0" /><br /><br />Sebelumnya, kita cari dulu solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-ztgGPDKeCVlVL5EHspXE0P9aVZCDmoMcmCGyarYLygv-HvSKA8c3z9fRr-8oHiRrEAWUT5ktI0eTw_7IDNnIClBIqZgXGPlq1mXlFxJUUlrhnNVqKLnBoYZQRjyHJu2KsdKf1QVlOmx3/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374944901139084002" border="0" /><br />Dengan coba-coba, kita dapatkan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihE7A8Y2sTBBJW_aWQ6HjD9rgL20EcSWMIID6HoQ1w40FmhhFBwu2ok4qj1atPUAflQY9X3l2yNoqhPgi26pcyLH7eifGprGIJq2gFHRB81fcaOTDFqiWMPnNN_hUuVJYSvnfDWVf4Qc9T/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374943659384908050" border="0" />.<br /><br />Kemudian, kita cari solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHOX1HfU4PwGpP_Hq4EoebaeH5kwPxQcfe4wLy7iwdwLxalMubf57Qr2YPRcV7QKLJuzu2Yc0UjF2BVd4Ha62SjiqLTy8YSTBmktW4ZfQLlj7uWqZvKH051tXjI8mheJWPgVp4cQJp5EGE/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374944909028599154" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYe4ghRpbsu14x4wWnQPLW5-9JzVDpf5GuprEX3bQr7JSqEWIQKwhPJv0b3q-IvBVYUU9czm6fGy7SoWvqmwNDvy7jqiXcFPhSeV4Ft0UKVz6GuGb50UvdDJABuyBDtA8kutZi6n7bwCxP/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374944886492252706" border="0" /><br />Kita gunakan solusi sebelumnya, yaitu 1.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO5AvGUgjwvGxnMozkG8eQMxD4ni14IhJjhTqZAri-M2fCsIwXlZ2QpSZnIC-VdWEN2u2O5OYZO_JR0WVWNsm4m9s1ozrlt76pc2Uh1KWrI9rBpWbdLETCHcMFmfhVBU7ozo7QKjt_RvDt/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374945916315969202" border="0" />.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGjmzIxI0UyUG3rMt5XSs3JmwrUB5cme6ObHZU40gbdrqQSAWtSZzYy5sdaagqXAQCGEaqr8XVaoQTmBo9iai9gl9OHV2g1Ilo1zrDXbnbD-UT-hAcPJ9Gdl_ucFqqxRyVdOvNyaWOjDVP/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374946519308982178" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (ii)</span> dari Hensel Lemma.<br />Maka, solusinya <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjGCFZCwT-EplhgjdXwb7N99N2rAAoS04RUM6rZ7mNzdDRqvks-ksa2qnO5okPmYbWr5slj_QIKtzGR12im_AdK-eD0CgxVS690mnbbcpm4o7RA9z5BBbVkSPqHieDH4FShZ-zbv3OYdFYb/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5374947353438565762" border="0" /><br /><br />Kemudian, kita cari solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMFF1NWswjQo502pf-lj1_3veESKIKg0elm5sGBfUhARvWdJoggJj2i81Ursc4mG8tNS-Q8TV2K-QXzLexFktjCTqW-BjUOL7BMt0T4zkNjMeFbNl-TRGmyi1CXh7ykrAdbaXvjON7hmmB/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374944891437074482" border="0" /><br />*) Untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6FOyhmiYxOOLq12YGtrL8DMsNfIVCuE0m8uft5i_B_hiuzeckFDKVz3yB09OML4aJCBEakPXBq1nymlXnZAicI-Ym5p1xatIXAkgCdl9FoCi1BhcflgHHQrT1YZ6ZAb-do_pI-JT1lxk/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5374947859744999986" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhO5AvGUgjwvGxnMozkG8eQMxD4ni14IhJjhTqZAri-M2fCsIwXlZ2QpSZnIC-VdWEN2u2O5OYZO_JR0WVWNsm4m9s1ozrlt76pc2Uh1KWrI9rBpWbdLETCHcMFmfhVBU7ozo7QKjt_RvDt/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374945916315969202" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgNYGSVj43JkBZ83nO0lhLWGGveycNHNqmiPNznssSV7k1OITZcwsu_5pjoCw6v6f4h3bM_wUYvcQhRe650SdWWLf71UVFnNiw3L6OWgomLi1UVE8JPFEs5ZAL299APh1jdt7nETYiDRo/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5374948949570851250" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (iii)</span> dari Hensel Lemma.<br />Maka, <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> tidak mempunyai solusi.<br /><br />*) Untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaYm0pEyYPMNh_kCBeG3Uoia4VVbWGyTqU8hnINxptOVjmRR3EVMoe4FyWSR_6uQkcayZQxEf5QVwmCNhWbHGOVWBkmVBZR_UzOTQUjg-Z03czd-nyNkXnFVlFvPDpt-1J8-h3nCuXzqg/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5374947843760366962" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilfNsbapNSAadgO79ooHaQxQIdbQH55nzjqshA9cw2dinlDdhK3Yisbxzf0TH8Fh3Tv41xZ9IY_w_T1g1A6xNXHVR3GGu2BjvsOCzS6WZar58uJwKKAD63tt-lBpwllMVUPa1_LEdEBWs/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5374949776615244450" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKrjEgBMDjQJoMvyg8_QcSFol5VP3V_6nzmAvWnFT-rmz-vMN8QVOXSTmDuIHRah18E_e7j1hkVQCtf9jaYPdmnEY8tiDEJfJSDq4koyVzSY4FzlMcvkSeYa5GlAMYBBfgoJWtq35QgDQ/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5374949770535540130" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (ii)</span> dari Hensel Lemma.<br />Maka, solusinya <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWQDMHqpk-nl4My43vIinwqVaUA_nHkZ8FfDr28fhZw410rbifWJIfM2w4VTtiUIRAmT7P1qb7_lOEJCC4EL0yYbdtOjmnfSiLLS-omPRPSe_O2uqF-PZ68wLAA1Mr3Ex57I8d4b6GDVE/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5374950393090153730" border="0" /><br /><br />*) Untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjCNjHpy__FHquiFydCyVcIRoR6V6KqDcSDFLVvRV_U9hgjNxeOlXVIHPB7gRjh84St8sWrX3cGILuIQWXWCfOsrybLY-tWVAfMp-_kmwUV4T4O6IvublM3k1xCG1B4_Tq1fI0YNtAndg/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374947834631475922" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiibiJADukcSs6_SQ4slYfTVAjy3nyXL6AFIIZBPyOXhvASN74o8rZXMTZb68tgmxg8B7jNgMa9GIiB285qAt04XZHdiTxGPPooE80NViAACnPjHP6FeegWFnhQXagNDQDwmAm11AFRwpo/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5374951254877511474" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxhhruir-a_fZNJRuPJMxJBB6jGtxaE3ifDd2jsw-EG9dohnQl5dlQ7RBPe59B6wtlG3cLM3oC5cjBexH5j5bRNlX8FYYdvdhGvk0RVT7MZs2hHkJ2vRjsxP6x0Gjjl_jbHkO5W6KkYQg/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5374951038888589922" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (iii)</span> dari Hensel Lemma.<br />Maka, <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> tidak mempunyai solusi.<br /><br />Jadi, gabungan solusi kongruensi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMFF1NWswjQo502pf-lj1_3veESKIKg0elm5sGBfUhARvWdJoggJj2i81Ursc4mG8tNS-Q8TV2K-QXzLexFktjCTqW-BjUOL7BMt0T4zkNjMeFbNl-TRGmyi1CXh7ykrAdbaXvjON7hmmB/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374944891437074482" border="0" /> adalah<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHO6e0cFpUxAIKS1ApPjHaAWJ_ykRUUNvOko95Z38Bt1aVtM9MjXgbiukZXw5o5opu4B3BjMPqSRDRBBuRaIO0x5TaTkJMaTc5E2U_KK13M8omFXsrevPOchKZl7BuMmdM0f4kHN6Of_Q/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5374951634741555090" border="0" /><br /></div></div><br /><div style="border-style: solid; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 7:</span><br />Tentukan solusi untuk <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-KM7xlyZjOcMLVkjTRBDm8IGt56h_PM-_1W9reFP0l5O8DZIcUx4PjBOBbXuDqtQHQ4QSf9Vsz3XOHX-C6L6MRWBYJEJbNUEs4qciobXKCm5CU1CkVbbhEAqH_TgH1TtTEB1DG7v1404/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5374952278290415906" border="0" /><br /><span style="font-weight: bold;"><br />Jawab:</span><br />Sebelumnya, kita cari dulu solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2y8SfsIaJkbz5dP14hQEssoAfifpw5w6ajEaS5zaZRR5hwPgyawfQfXVVVwjWUZFuzmyPgSNeMsQTKilca-G4wiD-XJDLXNJ6ut2bMOwNRcdN-BkyH_z2ytr8x3FwoPlHXgoG80IcerI/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5374953006414498018" border="0" /><br />Dengan cara coba-coba, kita dapatkan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjY7POvPCujGZTNfwTamarUcCO-31HvnO9KH8t2Of4G6qXRJ9YzhKTXZWRv-tk0cyWEvbiJEIkZ90W_6IJME9AYYrGkcwo0O_uAfvBba8OX5_wnT_kLHQgDfVk0vsiEUN4zcRxLvCXMftU/s400/23.gif" alt="" id="BLOGGER_PHOTO_ID_5374953524829220770" border="0" /><br /><br />Kemudian, kita cari solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglETKMoI-bxbDvkw0sNNSuqkW9Km0k2-L4lYwaqOU9Hsgt4iSCqTwNpSKYRWgtckDkl7E4bPVsR06nbb7JSe6a9pXOrhLsTYvPoeRtHdWubYlNK2MGPnGi4uaDvghSVNud2-pitXJ7Jzk/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5374953000739928178" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNHtZu7B70WAS1xgQj4EHa42Sdi33W_pj1OflFMk40Kyu_04wb8BFTfLC6q01k3kaQUjduksO4R2sZp9ghLmPP-cpb2DrDUKWrW3TiwA0VLRrCMPVAhG3wba9Q93W7_rT7rs_B8AEyEao/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5374952995867282338" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHBCpNZLj7vEs0Q3hTCZnYGpmbJXvuLah_17EjG63cen7cDnbDPoPznJ5lfw9OsKnA9X-_D0kIri-pv29P5IUUr-bWAqc3y8ZKpcPpJjhnLPc4DyoR4iiZmJUySGfGtkxeG65JSIzmTfw/s400/24.gif" alt="" id="BLOGGER_PHOTO_ID_5374954115643577986" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOeZD4TA9ZPgLnEmPHR7RWJYrp7UHnZFTPwxk2ctvKxighXJvL1j0fNfWeUK6Fj5KsMIIYuizJfpLuld0Kes9vtkU5GGFFfjN8ChlaYApvHDZ85u0mVOeknDBFHakWjvXgayr6s4hv3mk/s400/26.gif" alt="" id="BLOGGER_PHOTO_ID_5374955517497660674" border="0" />, karena 2 adalah invers dari 4 modulo 7 Atau bisa ditulis 2x4 = 1 mod 7.<br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYgoqcPnwRX7lF4MhbhXOo_-Jb5evYnwVZlxbhB2ayhCzaC12_cJFBMX7rAAR37AE9Qq5YTPHpRK0qb8nM1Zwd-AtWEsIQ5pPg-Vd_Vk4mjPRBtJEr2_69DovfJTkuSO2dESnEJks7b8A/s400/27.gif" alt="" id="BLOGGER_PHOTO_ID_5374957651910183250" border="0" /><br />Maka, solusinya adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9SpQCUBwEY0uMNND1UqHtBTbKCu1pwkflC4OPh-uhAoD3fzvMB5fahR5jqZdPuKo_ZpnuNaESH_ECpYn4cVRcj6_YQad0jdsWwdSOyFsM5mFP6tAjAR3dbMpqM2U0XHvv1tnjfwTJktg/s400/28.gif" alt="" id="BLOGGER_PHOTO_ID_5374958102389219778" border="0" /><br /><br />Kemudian, kita cari solusi untuk <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-KM7xlyZjOcMLVkjTRBDm8IGt56h_PM-_1W9reFP0l5O8DZIcUx4PjBOBbXuDqtQHQ4QSf9Vsz3XOHX-C6L6MRWBYJEJbNUEs4qciobXKCm5CU1CkVbbhEAqH_TgH1TtTEB1DG7v1404/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5374952278290415906" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2qVSquQYlYnBGD-XkEtMXQ94arbDb74jW4Y8gkw_DidBHect9Ci4z6bsZ2EU6Ftm_54NJ4eocPMhKtiVktx3rs-J5WY9u7SQnSwsJepQ4_YS6JLdw6WuoffU86i0px4nMu_Nk00N3mNQ/s400/29.gif" alt="" id="BLOGGER_PHOTO_ID_5374958783643873138" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja4ADeIUwWBFBlNNmEpIHQQvt2rt-7qX2fufkUj7wKiHgJfvyK7oa5Pr_9XyAEGuafL0g8T5FiouvE8yd3Rz-rU_VAMVtMVi5tckQIVyQFoUWrhvASdfu4Hr-mtBuqbpt_WuRKUx1FCic/s400/30.gif" alt="" id="BLOGGER_PHOTO_ID_5374959312224807266" border="0" />.<br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwq9sFZUXAvPuVz4uu5hVKUGYGdDuftXW-K0iqvwNSwEnfklMFrHV4Hn0AXxz0WA8YSgzT2XbJQiJOm-l4MRG8-emueMkb4YpGiFatgCeb29Aw4VHIr5z-IYOgT5dI4xuJJ1pP_KICARc/s800/31.gif" alt="" id="BLOGGER_PHOTO_ID_5374960583187695858" border="0" /><br />Maka, solusinya adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGz0WD_2UHQ69h_Bz7c385lyN9ljgZKpTcOZhxh_pAEkuQKBT0RUxK_CkF8kkwwb6_5U_i4w4DD47iTJzJnQYW6fPmmumM9RLkN11aUquJn94rM9pw0ETRlJPXQe8DJDsbIOHqoepst88/s800/32.gif" alt="" id="BLOGGER_PHOTO_ID_5374960576740884034" border="0" /><br /></div><br /><div style="border-style: ridge; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 8:<br /></span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX8WL_LhK-0vuLEVYj99jiSp7KA8H33VguUnLeHfHemQIapEQX0h2cXJsu7ZdoZYG0vozMvJ8M5pX8rUXlTJfiunMCD9oqpBj9wb8a29vGuyNHiNfBOVv6qpv3vYIrqgVEYcOtQEZkehLs/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374836206735516114" border="0" /> bersisa 1 jika dibagi 1331. Tentukan bilangan bulat <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> yang mungkin.<br /><span style="font-weight: bold;"><br />Jawab:<br /></span><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7PX2aZA_2X7zMlrf9_iv74ZPYtF_S3zYlr8gNK9jzakhPd9PcC3owSIbg7wU4KY_grCpIno1nVWst6YqzQdlTAR7f-OSaGGoJCYJsJYNYSUkQsgu4yHgX79piIL5wI87bs-LMXvYr3A4/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5374982537433282530" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7PVpIEkVCS1XX-_AsMN-4B8kZQSBdM_WryetaatrzTPtMYis57QQM0Qy_6BC7nT83U0abTrzs3iSlKggGhaujfJ3BX_-G40lDhNMzmQmiACm0bV0qJDIwpOxaoHENh7lVGD3fZojsyyI/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5374982508669331922" border="0" /><br />Sebelumnya, kita cari solusi untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBiZ55iEQzaPrqTjA0CXgmzd4DK20qq6_X8S9YWbwRuLROiBTmlLeoJjk6c_6VHWwsEhi8yUd81hfHH0U9rLjuUzVYK-05K7wKYqIRvDjmU7GrK2IWIzCAhMHgWqpy7b8Sc7ugXMo5mOk/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374982518595692194" border="0" />.<br />Dengan coba-coba, kita dapatkan solusi <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj37dLHq9D0i0lbGlPHgxUe8vf47JijwVFH0mIGKb-v-n8vTamuVAgV66w818NRhsyvheN387fqBRbQSeH9hWwmJ4mzpO86lovnkARm6Z__NXFa9bPHNs1JZeWd-tR9YCR86DpoIkEIsNs/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5374982368703314146" border="0" />.<br /><br />Selanjutnya, kita cari solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXihLH90s2AnPIUxNCbnm0eSi2oesPhmRNfLTkI10dqcDHS_UxCj4aDYhRyA5GlGAFXmRY0SRV9gmCELW6KNenQ7DjkQyFPUWu4ZhvhLgzj8ooPhP_xuiZIjgsILqQJ8kNTlqJlHuZsl8/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374982528039373442" border="0" />.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbc4vqJ-zNqxFTzheMpqZ5KXTTM1ewtLm0Xlt-o1oc1g87ouD7bXx4WVAxn5XDOIBV9PXxdF7NyKPTv2BAqQL_2ysx966OKjt0K8rKvsCDQgmnAWbPgSax9rgqMKGvwGuo84_3pmLwk0o/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5374982505410724018" border="0" /><br /><br />*) Untuk <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWMF6KJSOUkgOE5g8WZEuPjgqTb92P3WTae0z8PfKysRedDrG0wzhjKUm4Bc6vZDGMAs8sZh5c4tnxybYQ6xBEWk6wuXuDPxQEAJ3PlJlM6gdSoPGNnjNWxxJ0BpuN6cke4_kIyQaVksM/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5374982363388070306" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWgcIwjjLDkel8YWWaoDm1cLLwe3Dah2hBLOTVtKoUbWfUSJD4TvmJKeQS2zCvRekrWh3DqurQh8HjkYwH0b8GHFv26fgbMJfbQuTGXaYfpiJjPtVM2O1QzlynOSplnH2IdJ2CGakcIIY/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5374982353349524386" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZrTU70po1q56l3C-nYusPsO1Li65FZLFz-m9sl9uznyDzKUf_zqqtjprDLtvliJ0zkLqeK4LY4pvHt6JufjIFhkp4SwXNvNUKPwqPDFoawamCr80bFcBLIgKULZ1-LBw7PMcGeBAdgj4/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5374982343656173394" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidmEfmYmqMakq6ahv1hVEwZ1pkIXwJhkV4jgV4GMlTgBboH9kR7IbGDLLezHo6p-kMBHiUePxSTAcQydzt_qp9Mo1ISV6ErBiE4ol6Sk3ZckNHiSqzvqz_nkbYFTMGmUroON-OGgDyVZg/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5374982217709341586" border="0" /><br />Maka, solusinya adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbTxIPKVSCIQ_4JVelyVPlaa9rnzocjUFar4HPHv3NR8tPvwo2o2oh3UClosL_tyM0PPKO32FnQ8Sfl0lLR5cMHhgefxRbfEvh1cMBGeyQ3uWFrZWXvqN8f5TsfNryAA3yJTuwKNJBRRk/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5374982208784807874" border="0" /><br /><br />*) Untuk<img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNYKthUN3mORbHNOleCGlb0Bde5EWtMAn1U701gWylKQl6uf662gJBpTZQfaRxFX9kAXGGhA492r1VG4Hr6evgp8D3q30ndC-hv9E2CdIo5rc0v0Uk13XTGRm94-ljAfpt-ij0ybdlKB8/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5374982356156290962" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjFE8UhhbQg7AnLtDoisxAgFp6wwtSvsqQSrLjvJ26I037LorOm4o6LvSefNTsbII2h8KMIyVrohqHLwt5GluGoIx8Uhg38-Dl6J0Ft3tdpsa5NIRW34GE5tj0lwOzRIqr0gE3szniXC5s/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5374982200585751010" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9vvzBnm9lT4_yXAG3glRXExobkKeoZhWDWaOMI6zJ_WnEvrihpvSHZr10Pxyis6S9wph8X-01uh0HXn9txfHlO-Gg47lktEhKgqcJjkKoIIK0nyiPFZ_Zy3Sgvg3v9CL0Gg0LnYAA5-0/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5374982198006007666" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (iii)</span> dari Hensel Lemma.<br /><img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> tidak memiliki solusi.<br /><br />Jadi, solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXihLH90s2AnPIUxNCbnm0eSi2oesPhmRNfLTkI10dqcDHS_UxCj4aDYhRyA5GlGAFXmRY0SRV9gmCELW6KNenQ7DjkQyFPUWu4ZhvhLgzj8ooPhP_xuiZIjgsILqQJ8kNTlqJlHuZsl8/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374982528039373442" border="0" /> adalah <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBV5y6ROSZ_VNhO5c84AwjU51uGOQXvO6IZD3-s8k9-sTlHCb8iSi3BbdZt301sq_zZyTWTD63T6CsBtI8lh3e9lNnQa76qvzb2ICnZqcYj8IYZoZ9QTf373EK9-qXTuOQ0d7RxOyzYAQ/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5374982188749221970" border="0" /><br /><br />Tahap akhir, kita cari solusi untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXihLH90s2AnPIUxNCbnm0eSi2oesPhmRNfLTkI10dqcDHS_UxCj4aDYhRyA5GlGAFXmRY0SRV9gmCELW6KNenQ7DjkQyFPUWu4ZhvhLgzj8ooPhP_xuiZIjgsILqQJ8kNTlqJlHuZsl8/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374982528039373442" border="0" />.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEig1x5uptGNsrIuoPZbORHpv5f6aa15c7O9f_4Rzo0mGrFjRE8rISahjjYdU9hWIxnF51ecHR-3eoKiwn_pT52A1f_3GOvsrldMQtWjdpm2x2adyA7Imew5fFMKX_NdvKz-CeQOKbCfguw/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5374981993657427746" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZVTjyRd0YKf4K-ckx1kSX4gs1Z5yiGK5s4oQmEj-D11jEC5OCDfNJJK6lNnuJ3csIvsetWCg1ErnMspGK5J2Tq5dSN0qPBqILPbDHVEditfEEb373V4959C-90p87UmkFXORY-tV2LQ8/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5374981986706531986" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhEPyKsIPSGbqUKQoiFvyPv4OG8PR5RZGp5xVt45VBzJ0dfKU_KIqbdLFhEldgDrkshEm0GNbFIdMNA4wAf0AgdjFfe5c311ZceO8pd_N4dLj7CzBKrlGZjOkoeXwJZ2e4eU8ilJ_L09TU/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5374981983224945426" border="0" /><br />Maka, solusinya adalah <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRsJGKSvPYtDCwMYZqbkufAqY_RNz0xiuj2T0Zs7MLrd01jgKO5oaWZK5xZPGNWlI6eJwnMsYKyENe2Ne6A53huQ5mMhyTgK-HlBWzUqz6XGpOFoCg2ZfBXAd3RfrH3ixKABBYhG9Nc4U/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5374981973399075234" border="0" />.<br /></div><br /><div style="border-style: solid; border-width: 2px; padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;"><span style="font-weight: bold;">Contoh Soal 9:</span><br />Budi mempunyai sejumlah <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s800/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> koin. <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYXNrtP7VILqRaoYl5n_Ontw2sHkaK_zw8PRUtUpF_6gUDw8tkRbmSVrQP2ZexY-KQEJ3ttbKU_xyS0jorqoeZAYSCCnaK4obJ4JT76vM1L8gVLjWysmwxAwDsuR9xbuhH6rrgO7HmlE4S/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5374821797678119506" border="0" /> bersisa 67 jika dibagi 3500. Tentukanlah jumlah koin minimum yang dimiliki Budi.<br /><span style="font-weight: bold;"><br />Jawab:</span><br /><div style="border-left: 3px solid rgb(100, 0, 100); padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);"><div style="text-align: center;"><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihrNIBimrks9yZgVLiGxlXsZ7iMgSTa1KgsinrwwIg_vlOAtxgFsATgH3TwMtKfHCVtpoS11A1savxKth0xuuC4O8yCipReZgEoPQ-HbeHhsN14rjV4cAwR-T3CAdl-tBKurXwBjqb6KU/s400/45.gif" alt="" id="BLOGGER_PHOTO_ID_5375022778240011090" border="0" /></div>Soal di atas dapat ditulis ulang menjadi:<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9QFQVBnyx5Oc-o639po206rQov9DfDd9KK_2YmnMvh5c2bsLwIET-dEpHM9wBLo620uuL1P9jgqbE6zfdqwu7MMJbLUCRWyzbSXSQJSKopKA6qK2fAuWeHQXy5AgCmMqgThaiHyvr-mM/s400/46.gif" alt="" id="BLOGGER_PHOTO_ID_5375022772602462306" border="0" /><br /></div>Karena <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTdaFC_d49knLFT7zfoaLRBvsYz09dNf3eTEeWLMMpMVZTFJtc4FS7fukv2uWxXSaLryRxGx0od_fRxHObQ1-4BToFa7JT5y5I36zgtmV6MK69d5-AQ7gJUvdcKscLMR5ZWBx4sGJLbCI/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5375018841337478802" border="0" />, maka kita bisa mereduksi masalah di atas menjadi 3 bagian, yaitu:<br /><div style="text-align: center;"><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5-gF_asvBooiWC-FPAbL9WBAByUMq_VSptKGYKQx8oE0nBtuhLW00n5OOpEUwcBrc-6zBnGFp_8RScMZziOmRPNUUb93S1uRnWltc0WloHKGOhujNH33Pzux2CmdtaJConGdjkMtXu04/s400/47.gif" alt="" id="BLOGGER_PHOTO_ID_5375022229402969490" border="0" /> ... (i)<br />DAN<br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipZ8u66lXdfsjA7MdbajuDzXUTLwJ19dIKUytcK8otHC4xsgJ1VH-xHspuc98Zi80IfjGH8TXFkeFx7KL2VKeExE1SsAUhyqNCDmo5wch-e3N1EraJKfJuARzen_bSehWbwe2UVnfx9Pg/s400/48.gif" alt="" id="BLOGGER_PHOTO_ID_5375022226838729330" border="0" /> ... (ii)<br />DAN<br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2gqT5TjlDMc_DXhSZdIz7mbEme4SVf67lpzx64jgao2tw5cLFtWeejKKgyloqw9IvGP2pbrVu_Vof1-U1ELh9mC5BLDjVajDs5KRRpVoxQreqHri_0_psGihM1Yuu9Si7FXvlK08qu6M/s400/51.gif" alt="" id="BLOGGER_PHOTO_ID_5375022206340578658" border="0" /> ... (iii)</div><br /><div style="border-left: 3px solid rgb(100, 0, 100); padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);"><span style="font-weight: bold;">Tinjau (i).</span><br /><div style="text-align: left;"> <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5-gF_asvBooiWC-FPAbL9WBAByUMq_VSptKGYKQx8oE0nBtuhLW00n5OOpEUwcBrc-6zBnGFp_8RScMZziOmRPNUUb93S1uRnWltc0WloHKGOhujNH33Pzux2CmdtaJConGdjkMtXu04/s400/47.gif" alt="" id="BLOGGER_PHOTO_ID_5375022229402969490" border="0" /><br /></div>Dengan memasukkan <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgX7uJoeoK82cbLIbxNbpdLbDEIiUTvC8zooCCDHGt_WWNNBfgnThgxkiAXGdyWi3kdjCV5refftRAFVXrcbBb9ds6OlWk4lma1iG2DtkMboOWHJ2QHa9FeNTaFjrXWYpyfPbFdSqa3u-4/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5375018677548104162" border="0" />, maka kita dapatkan solusi sbb:<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFF_jtkIaZlHu4aiMqzokovvrutIjwmCnvcdD7D1nyMc5yYdSHFlBToOe_CRD0vQUqelwaoigp73txGwxIKsHOEQT6vWR1uvExYNM_d2VpLyuNduraAtGSNqEiFwmN2kAbOemCi-nSIAc/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5375018674411184674" border="0" /> ... (a)<br /></div><div style="border-left: 3px solid rgb(100, 0, 100); padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);"><span style="font-weight: bold;">Tinjau (ii)</span><br />Sebelumnya, selesaikan dahulu kongruensi <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihhCu-1_xMkmI7rIguXA2tyECYEpVLqwttfHJamTQ8dMTJfB7XRh6XE7zWnPnNzhyoIVHPdZGt6UBFGnBDFGUJ-BvsUHLGggj3bhi90Ob57wNzBAxVPFNF5MotY5Bm5-3Lq2MWOevEc9c/s400/49.gif" alt="" id="BLOGGER_PHOTO_ID_5375022216884725122" border="0" />.<br />Dengan cara coba-coba, kita dapatkan solusi: <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCB2PM0ppRTipXDbvaGx653dFnM9whKBQOxu9o1aQCG-Lf0xkRCq5-Tgm_obtTft0G4Zx4D0FE9x7z_p-lpze2tm3QYVXR2T2glPmpu654K1kbdnCR_dxKOsABLnVInNt79LVCx8jqGsY/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5375018443269522754" border="0" />.<br /><br />Kemudian, selesaikan kongruensi <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG-IDAnV2vPXlgDoTH-Xda2V7QCMeN1ojm5txbasGkb7QJx0JiNVrByyBzDYUtgtHqKg6bOlUU03Dt7RSQe-ZnKASzvtMnmgJu23D-0eZAOj9GfHbGhR5g6eIDR3iZb1nzo12J-3Xe7FA/s400/50.gif" alt="" id="BLOGGER_PHOTO_ID_5375022214144970946" border="0" />.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgEFVT3lTbR43CCu7sY2YW2GR9MrUXsQi0yj2TUgn_Xbu5FiKUGGlhmfKOtCbgGV7R7bHmQ1Kqj5Crg-HI3iXk_cg34cQ6m40jgKFuVL_QnXeHWhhvngxDcACjB40Ew9E2d9imWFNdTMAE/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5375018231386583314" border="0" /><br />*) Untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGGQ-JrMDBAQoxgnIECo2ZuDTxoTDSG8M8zstZCdgB4VxAUgq1g9agb36G0mds7CBsNbz-22dke8fjseUN24R_q7RsUflgtKCBe8FA0pv2MCk5quvD_dTo49SBY-TbHdpeewNWSah5CYg/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5375018439701659266" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRTMPvlZ8MtYhFfs2yIcqcks_1ejzLopoXY3PgUGjLmgD2uck4o_k6_EsQk-FdbF457WlQ6HnKJxfRt50SnfZ7kRTvPohSzvAG3y_lzR9KjOUh-2sUXPs_c3t4K19PI66x9jjRH__VbQI/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5375018228380536802" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqokpSxG8m2jU_mBRuJWsRSsKlQrBG-ZoKQibVk-vY2jFyFGEhtpAV-E6cizGUbNSBiWJJOaxvOLF142APepmZCRUqmWrCbeR5EWkrTgrwCSwaL2-iwKPlBXZNnKfWvzRQ0CYSIndE8_k/s400/23.gif" alt="" id="BLOGGER_PHOTO_ID_5375017910578595362" border="0" /><br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcGvvIlCf89Z_hZzCNfF1AxeVsXvYYm9b_ZAM7d0z1s5QZG2xxcSWAdS0zWGubCMalTxvqVVmmwN-SKfHAcPqWr4en3Ruyxs2vIXxaPSTMDZrOh4kirh87GL_WSz-IngOfLm2V6rgFlzI/s400/29.gif" alt="" id="BLOGGER_PHOTO_ID_5375017749647693730" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgW_JD-F2b7krfp-ycMaBgZYiPyWmRTFMNyZWLFMv7Kfbo8QnhwtrNj5CDMvztKsAzYkKYN-XWoNeSFXjcB5BnvzjxDddNO2ReaYd2TLPbN5KiiJ2cldUM7L4nWAtlGdMEPQSVJ5ehNra0/s400/35.gif" alt="" id="BLOGGER_PHOTO_ID_5375017488506402514" border="0" /><br /><br />*) Untuk <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBkrWqXKaFIzgrA2rcI-HCE_tRELmvsO966kPrvHChToo3Ee1XBdVMrO_rQCuCopaP1oc6mYRMarCly4W-EQ4PDyqGi8JNJ7Ar11vHEV6hd4MnJcBgDP_t0tzDVwjWQ7s63phdZT2jXgs/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5375018427559532834" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieXvmy5zQW9bRaY44iSrQdWItsW1KxPnamG9jr42-FGa_hORmP9droUPLNF_M32wcF6u5sIrPdizYKuLj9b2jJpoJ8d28b83PBV8C-BxI5faJIHISzYyA7vuMIFUeBb2WzGYFSDPxE6e4/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5375018219797151666" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIXR40Qz_pgNC8tGi4nTwYfT7xWJo3v-rjVaUKfa7lspCS5bQGJ5LJEmM2_0q6boDuo6peJ4LO5m7-BEu2hZXNR4y-WO1zK5TfH47l9aXKf6n37ETy11nVwpn9KIgicn86aUpTgGKYkIg/s400/24.gif" alt="" id="BLOGGER_PHOTO_ID_5375017905430666178" border="0" /><br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho1egN1oLSpNlt4FlKzPVRU9g7pSyQmWlCj-Fk_5exZTE5-5VNf2wvayvc3MBv5xNLNVGCyk9fhKhkX5bwg6P5a16ptAoOrW3kitIKCtvBMqLHBXDlAghQYTyyJxgtTG9dNwsoVmzL9q0/s400/30.gif" alt="" id="BLOGGER_PHOTO_ID_5375017746572723410" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgUiNZpF8KGseJ-IgPscjFHmPe8aukA4YnfOR-9MlZSogiiR5S0gbJ-DWHq8S1Ve0350x6mlDjVW5bn75QKB9pTBrRKwawS5uuba0gOnE8BIBGnYvlChlEz6VnIJ37pdSKXuCIpx6X5Hu8/s400/36.gif" alt="" id="BLOGGER_PHOTO_ID_5375017365666367970" border="0" /><br /><br />*) Untuk <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEis9ScFOsxy8R3imSzbLv_bIn-sSgoWHRpk8fK1s0h3npI69GeFNZI03vEkZU1XQaSV8RSKYtCY84q894dbWRsd7HhsngmA8GgisgYqy7EOAQb9vy6jpoICJp6pPOyJ6ECo6KLyYTGU1SA/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5375018419025940050" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg7xhAzO0s0Zqytdvc-wFBQYZnhKvmrghmDzwkCXlWLPrnmLUSxXQAl2Fu3NZah5JdZshR8a4aIZR2OXC9aM5Be8Hp7-KHDQEVbCx4yS5tmkG_mSPAdm07gFyzkJoA1DLEXpBSpd0Qjwlc/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5375018215572091730" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNuJxY1UuqDq6Fpdhq93OASqpv8h8RFSa6tu5lW_sDShxR-H-f2PCAijKqUT5bpn7FHK69XWdctpPInxi7cCkKlw-pIp-Y5xTNf5URZRpAGJFNFp3dZsgFWnrXWKydkcxwStD65ApQqEk/s400/25.gif" alt="" id="BLOGGER_PHOTO_ID_5375017897819551858" border="0" /><br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTWGHpN1kOgdDF6aiyX__bWqEZfhkn_6ZzgvYzDYnDuHTPW7-qA-RC-H_LyAfGnwJzqcN-cpCEGT6f0xAOGZQsFOnK53xHNFk6qBonGdpPRZlnWI_2EmDzlxQ6bbVJaC4irfn1R4VBXVY/s400/31.gif" alt="" id="BLOGGER_PHOTO_ID_5375017518766824882" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi76UbF0SYsJGUIRIGzZmAC2np2g61rpVnL6HYaGtTIUcEB7XOwXS_dgP0fXEndLtdq_4CquyzvDdmxpG0dL8A-ZwtEW13UG67a1PE939M3zLmaXyBP0xUzGIEE_RoU16UWIQ2TTMq8xpU/s400/37.gif" alt="" id="BLOGGER_PHOTO_ID_5375017359263025938" border="0" /><br /><br />Maka, solusi gabungan ketiganya adalah <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaPmwE5i3Rdyt2Ks9Gc7Qzyyy24ciG5Tr_N7fsISrsnVgUDvp6-ICLNjGg9PlDSJMBu8YbCa2my5aWEKhXQbabSNhDNxf2Mv0O_T8Y5BqEcIy_iQzXxz4eesJftv3EKXuTxpzyCtaj7D8/s400/41.gif" alt="" id="BLOGGER_PHOTO_ID_5375017126495026226" border="0" /><br /><div style="border-left: 3px solid rgb(100, 0, 100); padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Kemudian, selesaikan kongruensi <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipZ8u66lXdfsjA7MdbajuDzXUTLwJ19dIKUytcK8otHC4xsgJ1VH-xHspuc98Zi80IfjGH8TXFkeFx7KL2VKeExE1SsAUhyqNCDmo5wch-e3N1EraJKfJuARzen_bSehWbwe2UVnfx9Pg/s400/48.gif" alt="" id="BLOGGER_PHOTO_ID_5375022226838729330" border="0" />.<br />*) Untuk <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4pkjgnHZLdJ1y7-5TNWr0jTcj4dYWaiuP9hXY4Fdt5UEi8esZ4npnC6WIray3-5_vZU62Xnww2r4uETm9dskFPT0Pm4vnxypWIUV5PNJKf8uoQmqNa_C14xGnXQLMkgl3Ia4goW-n6Dc/s400/42.gif" alt="" id="BLOGGER_PHOTO_ID_5375017124414636674" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgs6Kj1jeLPannTlHly2CKXFxnkbFA7_zGLfdJGZzjytnDbFFKV3t6Q1iX60gJaINmmIfmQmnIFAMMn8Wsk1VBXUbrg2DjpTkCTuUC3dgtomtUVKkTIN2yOEjElT01C6nXbKyUnTRUgtuY/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5375018207347456210" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzJnwcpRgflIjNy3Dx2MuGDjJ_gX6Ck36Vymypd32M4AQHa3sPwNDSzr18B1UskJZP16XzlbFfU57hKd5s_32dA_IjhyKZgPrw6EBG8vo7gfZerEzK1rPC6KeM9Fye7ONF2_bHvxx8aDo/s400/26.gif" alt="" id="BLOGGER_PHOTO_ID_5375017772969905042" border="0" /><br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDo1idYMZlfLi2s4wJpR46zwWPGbRjnfgjQK1_TEO3KQItMzJo7sscxVhhGVGGjr4JGbjQEiAquJQRlheeolttBX-HxeOcBPaZlMKrQL0d5fyhAoI1eCG0pQiHErj-2K9GjgTgCrygnJk/s400/32.gif" alt="" id="BLOGGER_PHOTO_ID_5375017510275462178" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh73db0ke571DpQiE11jAlz-iVpjL0C2Q08kBDaFc-rQiNIxnjgohU5wCWBUxmOAedgVFk1fmN-ls38AnwUVx31Xkegyq5fscQZ7fiHre_QDcS1rgYb78R0ZdeON-OHQlOzWjzGVtEZ3vI/s400/38.gif" alt="" id="BLOGGER_PHOTO_ID_5375017351984238066" border="0" /><br /><br />*) Untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyn5Xb1X5COweYQ8HuQj5SdYF3H3fFBJYiXo87vJ_pEHJRRfLDvqCa05ug7oyQicP1vtb7iLrjg4NtDzE9Y3crpgAb808mIaiWreFBKk2Q5les-mUWhkpsWslHdsS1bhia_BRA1a7-98Q/s400/43.gif" alt="" id="BLOGGER_PHOTO_ID_5375017117131202290" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgC-t__g0BhrKUwRQdlhwsDXrrBLmjDul54TgFYUKWMhI8AvV2hiCo5TAT5m-ShUaMnQNNaugUGdSdItgdMm3knSQLmRnXuRNi9VuCZrbdC7lRJFS-auSjGKrgCqNAJS5rI0F2cbmofc2c/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5375017922096466866" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzLvGssr_wT66Xyb4wDZ8EibMn_B8RCSBVUs1-lsdArCb433xVj5M4cwv8kW0-q3WKKwlFjtqcLLDSW2q7jRVh9HnY0NPPKD3hohLp-3sr15Ig5ZLvROOB4SrRdhFO7cuFTkO48rdN2ms/s400/27.gif" alt="" id="BLOGGER_PHOTO_ID_5375017762842977090" border="0" /><br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYlqB826u8C2SsRkzM8jVWMRYpZ2z0qXJVt5_kDwZeJWTJAjVc5AK9QwaBlEzXa9-Cm8hyphenhyphenMfM9MBoE2n3vFKYRH24hzQJBSyBGbi3uyj1zY8YWO164cTXCrMJAxvJByK-0mgjUE14_pGg/s400/33.gif" alt="" id="BLOGGER_PHOTO_ID_5375017503998658866" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi91Bh80zzhKqF1WOdUtY2SEoG8HPYAkwVmIIp1NbzHjMtJNOoMZKaDPyWjIbZUFfay-dkl5QrmQcELEpsTqehyphenhyphenmoTGidGauVj5qteEIV5gg3hFdebFpQFk_XAiWynhDAeogtWJPydyDck/s400/39.gif" alt="" id="BLOGGER_PHOTO_ID_5375017348697654738" border="0" /><br /><br />*) Untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQt7X1SIUIuDQRQay4SYly9AayA2S0TwLV4IDsWNdJGNx0w8x0-pflLV5UJVW9qCyqtgit-df3tl4y1gD9gDd_Kl_wwy52sX9l-FtQMR0b6z8my5lq9fKaJPZ93i-F-Ks0YBgynMOe-5k/s400/44.gif" alt="" id="BLOGGER_PHOTO_ID_5375017108806241650" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-Jyz5VyQlS9s95cjw0Kn7l79wOoeUjogTFiHnXp_lEn3XD7uqPuR8zwOBL_en4oFB2jWriXoeQ6IfzWv_DVGacqn54KTzagt4JLLOFXdyMgM15tFNDubDZ3oLVEC6tMivRPZYjAbqmWc/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5375017919009893474" border="0" /><br />merupakan <span style="background: rgb(235, 151, 248) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;">kasus (i)</span> dari Hensel Lemma.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLlmNfR-zCBufCxPZYBJSWuoFcN_k_2aSb36cTl_qXFvXCec_73J8aDsMMWgsDadlp4OI50f2wl9jJuVKNz2MipfbLNQQBGMrCwwA55RwMxQvtKzkq2lSa9ip9Y3Cow3-PBPSVaJ5lBmI/s400/28.gif" alt="" id="BLOGGER_PHOTO_ID_5375017757241286322" border="0" /><br /><img style="vertical-align: -11pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgh7KxjBaUQjzTJ6YJN9pjLp5XvOHmAjQK224USiCivh-uN-qBxfS486Rz-rT2-V6nYIgYK3t0cUdMGAGnIFp8LtNxwh1C3YgdM2TLMtl_gCf2dXWoZSLSsl2SybGoJvc049reMM6Y6t8/s400/34.gif" alt="" id="BLOGGER_PHOTO_ID_5375017498895884722" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKIwBCmVA98vbrKUX2pD5v8aQFKQYsSMpc-SW9EfFK9hcUDesEqLPUjza4ATpgBUj5odvxaRTyaJ7ElB8reV5LHPZuPE00fiPVtWi9KNjIzEClZcFJNM8X0rX19UMvSmHjiCAfYqN_Y7A/s400/40.gif" alt="" id="BLOGGER_PHOTO_ID_5375017336564814210" border="0" /><br /><br />Jadi, solusi kongruensi untuk <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipZ8u66lXdfsjA7MdbajuDzXUTLwJ19dIKUytcK8otHC4xsgJ1VH-xHspuc98Zi80IfjGH8TXFkeFx7KL2VKeExE1SsAUhyqNCDmo5wch-e3N1EraJKfJuARzen_bSehWbwe2UVnfx9Pg/s400/48.gif" alt="" id="BLOGGER_PHOTO_ID_5375022226838729330" border="0" /> adalah<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz1qY4ATJ5H8b92Nl29VJYjrgxjvy_jLcDeS6kbjTtSGedWNXKf4dANk8Ta7usGybwHEUTZxm1J_ICfMIukCM2J3qvhXB1QO0-ob36rURXtX74tXeIsvbzeFFTOUdO1izBXusnyJNZb1E/s400/52.gif" alt="" id="BLOGGER_PHOTO_ID_5375028426092161954" border="0" /> ... (b)<br /></div></div></div><span style="font-weight: bold;">Tinjau (iii)<br /></span><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2gqT5TjlDMc_DXhSZdIz7mbEme4SVf67lpzx64jgao2tw5cLFtWeejKKgyloqw9IvGP2pbrVu_Vof1-U1ELh9mC5BLDjVajDs5KRRpVoxQreqHri_0_psGihM1Yuu9Si7FXvlK08qu6M/s400/51.gif" alt="" id="BLOGGER_PHOTO_ID_5375022206340578658" border="0" /><br />Dengan cara coba-coba, kita dapatkan solusi<br /><div style="text-align: center;"><img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-6d3gv_BlaYPSmixt6c29IuwbyQdF0bVoEP0KUHlYAxSvinvmLVAaQW_t6avqwNOVrRQT7J2zCZTcwagZ1LxNxsmIlXbTjxxtB6VYMeHbqLlWWJgBfrRZ1vTzTCemSkywO512A84fcMo/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5375018418141614946" border="0" /> ... (c)<br /></div></div><br />Maka, syarat-syarat di bawah ini harus dipenuhi agar solusi didapat.<br /><div style="text-align: center;"><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFF_jtkIaZlHu4aiMqzokovvrutIjwmCnvcdD7D1nyMc5yYdSHFlBToOe_CRD0vQUqelwaoigp73txGwxIKsHOEQT6vWR1uvExYNM_d2VpLyuNduraAtGSNqEiFwmN2kAbOemCi-nSIAc/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5375018674411184674" border="0" /> ... (a)<br />DAN<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiz1qY4ATJ5H8b92Nl29VJYjrgxjvy_jLcDeS6kbjTtSGedWNXKf4dANk8Ta7usGybwHEUTZxm1J_ICfMIukCM2J3qvhXB1QO0-ob36rURXtX74tXeIsvbzeFFTOUdO1izBXusnyJNZb1E/s400/52.gif" alt="" id="BLOGGER_PHOTO_ID_5375028426092161954" border="0" /> ... (b)<br />DAN<br /></div><div style="text-align: center;"><img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-6d3gv_BlaYPSmixt6c29IuwbyQdF0bVoEP0KUHlYAxSvinvmLVAaQW_t6avqwNOVrRQT7J2zCZTcwagZ1LxNxsmIlXbTjxxtB6VYMeHbqLlWWJgBfrRZ1vTzTCemSkywO512A84fcMo/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5375018418141614946" border="0" /> ... (c)<br /></div> Perhatikan bahwa syarat (b) adalah syarat yang memiliki angka paling besar. Jadi, solusinya pasti ada di antara 3, yaitu <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmS7BpjnZjN4cJU6wyj1bXCPgGBLo-SzsHrMZdpJXLHVo3JwvOpUhSIwKrvTeQ3p4BVzSpIHFBuEXPgCyHBy-3f69zzFm8SReSPz0dby-lVAq3QSMSuDsTm3r_IhHsk1mc3HBB6o4mXcE/s400/53.gif" alt="" id="BLOGGER_PHOTO_ID_5375030266600619842" border="0" /> ATAU <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnTwFPzNUE6AyPhDYjm561VcrNru_jR6ea6cVsr3asM2iqwr9I2iRvx5MoH17LzHDzRgp7plqYuMGyounQN2lnS4RwKLWyabdRdrqHm4MhzVEO00hQhZKNc7wlvFskCMTO6pBiszw-uPk/s400/54.gif" alt="" id="BLOGGER_PHOTO_ID_5375030258353978066" border="0" /> ATAU <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR1ezUc241m9ZJARV7RyIbl_ObeCT9s6YoOFlGTJ6xzz9rz0PxhxtQqu2Lt5HkfZdUJqPIFB1_m-wdZ4DkrnzRN5faeHCX3XfvbKyAGVTJmMwZbbvHEQp9-r1Q4NaQXNV4mCiyGyvp6pg/s400/55.gif" alt="" id="BLOGGER_PHOTO_ID_5375030251288942418" border="0" /><br />Perhatikan juga bahwa yang diminta soal adalah <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiYE3erKxJ2zk3agXH0FcDZLgSfz2_A9bAzhGV2ZxIV25am7lCw6xKsNzlPnLd_ct5JkbPwTH70KKXciBGz-IX3CO5AGL4uzEArOqYh9lvM1p9UoBGW-ilVpZ8OXUgJMh4X0QvPOOIb1xGi/s800/2.gif" alt="" id="BLOGGER_PHOTO_ID_5374819600432751234" border="0" /> yang minimum. Jadi, kita akan memulai pengecekan mulai dari <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmS7BpjnZjN4cJU6wyj1bXCPgGBLo-SzsHrMZdpJXLHVo3JwvOpUhSIwKrvTeQ3p4BVzSpIHFBuEXPgCyHBy-3f69zzFm8SReSPz0dby-lVAq3QSMSuDsTm3r_IhHsk1mc3HBB6o4mXcE/s400/53.gif" alt="" id="BLOGGER_PHOTO_ID_5375030266600619842" border="0" />.<br /><br />Cek:<br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmS7BpjnZjN4cJU6wyj1bXCPgGBLo-SzsHrMZdpJXLHVo3JwvOpUhSIwKrvTeQ3p4BVzSpIHFBuEXPgCyHBy-3f69zzFm8SReSPz0dby-lVAq3QSMSuDsTm3r_IhHsk1mc3HBB6o4mXcE/s400/53.gif" alt="" id="BLOGGER_PHOTO_ID_5375030266600619842" border="0" /> memenuhi syarat (a) karena <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhShVazymHCIsrHLP6hs5-Q7KCHFZ3kvhnOSuj-CjfynVFGdXWITGLvqOA1n8d5q8Wc53CgbKQXLupugNjX1Km6Vivk-iRUzZp_rR1_KMKDTlgs_gOsjoidTUN6h-HLvMGdHF0VMe8Zdgo/s400/56.gif" alt="" id="BLOGGER_PHOTO_ID_5375031330932654914" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmS7BpjnZjN4cJU6wyj1bXCPgGBLo-SzsHrMZdpJXLHVo3JwvOpUhSIwKrvTeQ3p4BVzSpIHFBuEXPgCyHBy-3f69zzFm8SReSPz0dby-lVAq3QSMSuDsTm3r_IhHsk1mc3HBB6o4mXcE/s400/53.gif" alt="" id="BLOGGER_PHOTO_ID_5375030266600619842" border="0" /> juga memenuhi syarat (c) karena <img style="vertical-align: -2pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQfCqREJj1peztgY9Zvu2sWIS1XY3o8uv5coeJ-YHWH-cOzwSLEQlxPOAIuGW3sQelvRPUc-bq-asdRn-2X3F4mzw5ee9rZujXn_xO00UMORD2Lf_qcfotszw7MLS9yOsBj4ExT39CMXk/s400/57.gif" alt="" id="BLOGGER_PHOTO_ID_5375031324312248962" border="0" /><br />Oleh karena tidak ada bilangan yang lebih kecil dari 69, dan 69 sudah mencukupi syarat yang ada, maka<br /><div style="text-align: center;"><span style="font-weight: bold;">Jumlah koin minimum yang dimiliki Budi = x min = 69.</span><br /></div></div></div><br />====================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglgXGWEfAeDUBwSqOYoLY8gbvfCrlD053wUVXJAzsMRZwmnfk5X_tx5rlFiq7xWpfHRA1CWQ0oYhIyi-rlAmSb31PtQm8bwB8kapJ2zyzSfH0hrXzIrL6B0ur9s2mBw2NSArjdiBMkG4Y/s1600-h/judul2.jpg"><img style="cursor: pointer; width: 139px; height: 23px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglgXGWEfAeDUBwSqOYoLY8gbvfCrlD053wUVXJAzsMRZwmnfk5X_tx5rlFiq7xWpfHRA1CWQ0oYhIyi-rlAmSb31PtQm8bwB8kapJ2zyzSfH0hrXzIrL6B0ur9s2mBw2NSArjdiBMkG4Y/s400/judul2.jpg" alt="" id="BLOGGER_PHOTO_ID_5374992310043412498" border="0" /></a><br /></div><div style="text-align: justify;">Sekian dulu mengenai kongruensi modulo dan Hensel Lemma.<br /><br />Untuk mengerjakan soal ini awalnya memang rumit, karena harus mengenal hampir banyak bahan dari teori bilangan, seperti PL diophantine, modulo, invers modulo, dan CRT. Namun, sesungguhnya soal ini cukup mudah. Untuk memahaminya, kalian cukup mengerjakan semua latihannya.<br /></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber:<br />1. <a href="http://en.wikipedia.org/wiki/Hensel%27s_lemma">http://en.wikipedia.org/wiki/Hensel%27s_lemma</a><br />2. Buku Elementary Number Theory and its application by Kenneth H Rosen.<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com1tag:blogger.com,1999:blog-8125318493233557109.post-86128840236714188092009-08-17T18:10:00.043+07:002009-08-18T22:12:17.719+07:00Lingkaran dan Lingkaran dalam Lingkaran<div style="text-align: justify;">Soal-soal berikut memiliki bentuk yang berbeda-beda, namun sebetulnya serupa. Mari kita lihat.<br /></div><table border="0"><tbody><tr><td valign="top">1. </td><td>Tentukan perbandingan jari-jari lingkaran A, jari-jari lingkaran B, dan jari-jari lingkaran terpotong dengan pusat O.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsg0j3JAgH-j6QZIOO3Aa2yybQTyPh6xE_Xxo81nJqSxhF8DcAwlshXUWjIi55qy2QveGfsLBuHhdik9EANoHUyDtjC7dpX7EUodHLyVHZFyWhl-ykrND-IOcdxOZ5HMpqkuvCHa1idVMR/s1600-h/lingkaran1.JPG"><img style="cursor: pointer; width: 274px; height: 241px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsg0j3JAgH-j6QZIOO3Aa2yybQTyPh6xE_Xxo81nJqSxhF8DcAwlshXUWjIi55qy2QveGfsLBuHhdik9EANoHUyDtjC7dpX7EUodHLyVHZFyWhl-ykrND-IOcdxOZ5HMpqkuvCHa1idVMR/s400/lingkaran1.JPG" alt="" id="BLOGGER_PHOTO_ID_5371136833750999554" border="0" /></a></div></td></tr><tr><td valign="top">2. </td><td>R adalah jari-jari setengah lingkaran dengan pusat A, sedangkan r adalah jari-jari lingkaran dengan pusat B. Jika BC tegak lurus AC, r=5, dan R=7, hitunglah a.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkYHZnnfKZ6X6e_cgFm7wPV7gvDJwDeoCJgh5lh02_yXzdIhrHRnibNGMK6aHQoWEvEEEW34qpSU00yeVXAzearhY0QZVUgqGhMhDSaxEefyiLWIsF-mZGBTW_kf2caRoZlV92eEtyCruf/s1600-h/lingkaran2.JPG"><img style="cursor: pointer; width: 400px; height: 220px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkYHZnnfKZ6X6e_cgFm7wPV7gvDJwDeoCJgh5lh02_yXzdIhrHRnibNGMK6aHQoWEvEEEW34qpSU00yeVXAzearhY0QZVUgqGhMhDSaxEefyiLWIsF-mZGBTW_kf2caRoZlV92eEtyCruf/s400/lingkaran2.JPG" alt="" id="BLOGGER_PHOTO_ID_5371136830636771458" border="0" /></a><br /></div></td></tr><tr><td valign="top">3. </td><td>Perbandingan jari-jari seperempat lingkaran B dengan jari-jari lingkaran A adalah 2:3. Jari-jari setengah O adalah 10 cm. Berapakah luas yang diarsir?<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5FdvuvEbxFbQmJp9raDnnxNWNZBOJ1RNJxkFeR8vQr7quPhibfiGKx318L2z-0iFz6TWiv0zuLBMlJipNTPHFJI8PIeWLtftyefPh4xTHr3Zg3JsK3csJHF6Dybf_jMfwPOU8uElKc6M2/s1600-h/lingkaran3.JPG"><img style="cursor: pointer; width: 400px; height: 219px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5FdvuvEbxFbQmJp9raDnnxNWNZBOJ1RNJxkFeR8vQr7quPhibfiGKx318L2z-0iFz6TWiv0zuLBMlJipNTPHFJI8PIeWLtftyefPh4xTHr3Zg3JsK3csJHF6Dybf_jMfwPOU8uElKc6M2/s400/lingkaran3.JPG" alt="" id="BLOGGER_PHOTO_ID_5371136607417865922" border="0" /></a><br /></div></td></tr><tr><td valign="top">4. </td><td>Jari-jari setengah lingkaran O adalah 15 cm.<br />Jari-jari setengah lingkaran A adalah 10 cm.<br />Jari-jari setengah lingkaran B adalah 5 cm.<br />Tentukan jari-jari lingkaran C.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMnqv01oZZuotvO8Qt76uHZALjR1n4va3voQX628tQfAXFf9juaSyybXVkG5DhNMxE0twQIZW0SGtfbXdsxZ2Kr5ZFyMEj_Xh6Ke6VYcOk30LmuL4uiKiBDkWvlTN1Nqeq_85zV7HSnCzO/s1600-h/lingkaran4.JPG"><img style="cursor: pointer; width: 400px; height: 225px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMnqv01oZZuotvO8Qt76uHZALjR1n4va3voQX628tQfAXFf9juaSyybXVkG5DhNMxE0twQIZW0SGtfbXdsxZ2Kr5ZFyMEj_Xh6Ke6VYcOk30LmuL4uiKiBDkWvlTN1Nqeq_85zV7HSnCzO/s400/lingkaran4.JPG" alt="" id="BLOGGER_PHOTO_ID_5371136598550507266" border="0" /></a><br /></div></td></tr></tbody></table><span class="fullpost">=======================================================================<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX6SHbt9CjOk7V3R9uM2nR2Psr75RBwZtNm8Wl5FhX_e32_0giuIK6Nm_CbCx7h2uC9lxneFD2cVNXY7N84BM-eZfVAGayUR0zb4Gqid-zJQG5stee5cutnHXbGMo7A36I6Om7wmApHGJw/s1600-h/judul.jpg"><img style="cursor: pointer; width: 183px; height: 18px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiX6SHbt9CjOk7V3R9uM2nR2Psr75RBwZtNm8Wl5FhX_e32_0giuIK6Nm_CbCx7h2uC9lxneFD2cVNXY7N84BM-eZfVAGayUR0zb4Gqid-zJQG5stee5cutnHXbGMo7A36I6Om7wmApHGJw/s400/judul.jpg" alt="" id="BLOGGER_PHOTO_ID_5371166844242674130" border="0" /></a><br /></div><br /><table border="1" width="100%"><tbody><tr><td valign="top">1. </td><td>Kita buat kembali gambarnya sbb.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiU5fm6PRfNfyLtNH_lTo6av7DVWlV1E72AmtxuVA_dr822hfUgMmDFAhnnBXuX1DJiJvN31rqU7qRDCNaXWSdz_QygZFI78i5YU-zDSpW5YatzYEy6Ewps_7DXkdht2mN3AvKrFpQo01fw/s1600-h/jawab1.jpg"><img style="cursor: pointer; width: 286px; height: 240px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiU5fm6PRfNfyLtNH_lTo6av7DVWlV1E72AmtxuVA_dr822hfUgMmDFAhnnBXuX1DJiJvN31rqU7qRDCNaXWSdz_QygZFI78i5YU-zDSpW5YatzYEy6Ewps_7DXkdht2mN3AvKrFpQo01fw/s400/jawab1.jpg" alt="" id="BLOGGER_PHOTO_ID_5371167450468289202" border="0" /></a><br /></div>Karena <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguYv2eYCXQwkrRwByOnhXazr97_vAfWCpN2L1MQ76BITH1JONRBV1FdnN7yXoAJt5NetLwzMSfMmkzYGjXpPYcHUPKCX23BOZwWGYTVi3BHHldAu5Bzqf2CuRwvhhn8W95lYQfXLgK5GMe/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5371177978254496754" border="0" /> , maka<br /><div style="text-align: center;"><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjihDsrWMWQvTQSlSxtmCKtFFjiQoQo-Cnjach5GqCQZP4BkiDd_e6LIYloVWlVa2hxKI98PIxmPM1JusYpAMLK4HF57aWgVLYLg86544iFTXNlak20_vdZUi3IbfjYtIOdM1YshRFWqHzH/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5371178400334248562" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAcYchhRsuxiGqlEkWd06xDEQkwUvz7XCb8XjTm96DegxWzyaDWMTXal3IFcfhm6Hh102cZfHWrlDDDj1GLUGCF2VqzEUEHHhRMl9AQzHS4NHJJ30CY724YbQ52rfTmtnaJ5Gd2sTqfhCb/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5371178395280974018" border="0" /><br /></div>Misalkan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2NBayoWGtGAIpzr0PhM08wS-aw1e2LjD2rOu8i7TwpIASNE-cKP8RjkIgjhyphenhyphenVMDpSs3PzYmEaASDtlbpRkJj95l5szxDVQOeg4orPc7bso24SudFgVgEVSTzlQ24wZIkAHrxpz56JsImT/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5371180126847310610" border="0" />, maka <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhywjuYUktidXOK84xV8-euukpe5tt5U8Ar3uPZ-heuihDUxxV7PUuvyt2CfGwxhhulswSi9xdagJ-4pOtEGt0Fex7oXkGDx81yBHdkhn1LsJjNHeU5DVv9TyvrQSZmUcubQq3ccMKota37/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5371180124077756466" border="0" /><br /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaNGQeSmjeKaQO2M0cbUJ7HNYRaCzuBHgIsohs2A_93a3UrOiwZr_ECle3Gkbt-XkscKKr5HObducJTgukpBVv9gyW6keYO_lM4nVC9VBDgRbRj4xKq7xjfEgx_9UuvpN-XUSk_dRb3fQL/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5371180503021076322" border="0" /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1cUvJjOaZpZtxe13rIsKqSJ_bzhbjESaBwj9cJWB9xUWSPyNchaVs4slKcNJmV4u8T_xlnLaYzGbRphdbU7d9je4v3aTtsPYtLOonwpPP6Z2Xa8mIfsBR962vhCl1d9LoH6gLiqmo3umY/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5371181180246438354" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgC9ELIwDYFbeACuVOytB6qJti1TzwcrjX0Oc2rcuZvbLA9zbYe9_03gsqOa3_GTNEbuzqjzHG6M6mEi3XiujdG_4bLLkvQwFRPXRtAkCPyvEjQLXa_Sd5TjkAFX6NX4ILgOj8JclLJWbJp/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5371180498994862466" border="0" /> <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgfBf5iDzMRyCH6fkutn88S6UyiZUn3GpMkRma7kl6B7hAQkCUu7gYq_-HNTdP8ti5THQeuB7VIZkM2LGFf_CXATkcJRNVkTyaS80A67U9B8BxoIC5Bz_pgLsYBQlll3mcMgXdK0gKbC2YR/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5371181171908885826" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_Ujy26u73G_npj8jcmv4hDJiUP9SXlFCbn9QOEXep_Lohpj-vFV0w0VRaIDl6HQ1hSWLa4xT5nbP5RrtWYUSjC0zaEgSgSXCKRRpbX33tx8Xe3efOTMe7Hqec3r9n7k9YGo9pbgKTUK7m/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5371181787171722786" border="0" /><br /><br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQQYs9UG4jpuz4LqWzKKib47qGhxnKPAWM5Os1hKm9_XV_r182Ck0xPMToj0LgPFKQgg8k3U_1ck-4j2zVSqXrOwXEPHlnCiSOgy8RqnpAiYpFdpWCy_tyi7mrEX0Sv3ka-m4r8Lllc5HU/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5371182463845801410" border="0" /></div><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzeGwVBTqHz8YBkEOiMJzucZpCZHaF3cPVAZGULxAjJsmKGSIOVslXMb0z0DdknwDrFediuQn37bjO9fLv6PFf-McWUp_GawOtutMYejPsYc2qaRKJu63oyZBCM2cyJZh3h5hGjDmrbo5X/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5371184402592879426" border="0" /><br /><div style="text-align: left;">kuadratkan.<br /></div><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP-u23zYVs3m64AWZPx_-8LAQjhapbCpbiUF3RXtpBEfxwQd2rUdXRS3brXI3GWqIdPDRHNYqvHnCCEQppKyab9ett5Ov_id7YnVyyPfMdb083PKKkVYKXi5DvXI94cWkOr48T41DSTmsn/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5371184397001853970" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgl2oJmzu1GcOdu8w9k7qu2XM21ISDz1aaDT1r32hmFQ2e8jMsVh_Z43epJf8Cnz2GCz7_I7tU7kyyrnD97iHMnGKrUAxXaEsVfXbYhlIAV6aPpuZC0B8GSAXRAgxYx6cgH6GXJuSs9Di8R/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5371184387962163682" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXbdvadZka9DzdZV2qfVi9QtrnJTXGRo9ZnGa-K8QNLI69XMPG_00V6J9dOdwyfCSLF3iygGNeZ4cyG730GDc5HAl5Bu71lbhhbp-trtcn6dSLx8GxVtXwtFynVrX6m-GoeSkTEOtjmn9y/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5371184382656282098" border="0" /><br /><div style="text-align: left;">kuadratkan lagi.<br /></div><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgR3bzbZ0P6089XqtXEhUkfOzj-69CphIKD8Z5-l7RfVKdXIwNGcVcmGrzmvhtye9doKP5Y-TzJjkDvwjtgUzOz_qAZMxblnrhpwCMYUm0JEKNKfkpHL-jsQSQA4LJ9wabcR8ZSJTvBWQV4/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5371184376644333426" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRzNcuJHE9vyB94kyhz7pjNo19xCiddgbcH6SH_iQME1DL5k8r4I5dc68P3bTwAQ73ERB0IYFmt24I4OlqMAzE1yA6F-Iac8fYL7n960Mew4eOEqEWAcscSTMBWyRqyFbm8gEEZXwIo6Ep/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5371183954104980706" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZgkJ1EZ4xAkg77BEoeIitykia8WOrtx5DibA4pcOeBD4CYgOkYf26bhyphenhyphenguOSqWEt6XSynU1VqOUSMV0e2gkauxOA8enmLwlMxUc4N8UPdR5DVIshDqAauhVSD2dhv0MamIxdNd9xpSG1Q/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5371184224440124658" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj11I5A6hFIxEz5itJPJ_MosYfc7jNoL9HGuRu8M_EBF-DFQuSOSdcmqla5qU2lIXZbP2b9bLVhcER-dpIpSinPRO5FAhhcLGSb4CkgTHK8gsAC9OTDa80PtWYqg7ZI6bz4AIlxHrgdx-1h/s400/22.gif" alt="" id="BLOGGER_PHOTO_ID_5371183943083828546" border="0" /><br />Pilih <img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA8XwEIYl-PQRQ20D3CmCbIJvDhMmizpWevSu45ksgiP8aqBHp_CEQXXmQ-2L6748rfRBNShAjVU3jNZUJaGbgiYmCRt00GK_SXOtvwLIToRsytuvi_TsAVY6-aSQg6Ac1cNFubzM2TKO5/s400/23.gif" alt="" id="BLOGGER_PHOTO_ID_5371183935120685650" border="0" /> karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIpoVsPla3ahwszRy3KjNhyphenhyphenufdojLy01NURFHtkObT67UhjhiHtLFYb9sq_8bPbSD6UiQwY4iEoGEy2uLmkpY2OTJIel0TWdZAOJ1WeQOb68HMwlpy0EsVDyg2tpTXL5P_6DYyIqxrNgeO/s400/24.gif" alt="" id="BLOGGER_PHOTO_ID_5371183930688279314" border="0" /><br /><div style="text-align: left;">Jadi, perbandingan ketiga jari-jari <img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheAl1Z9xYBTbdMmQaoGu02uexFcGaxrFpD3wwkSHsp8XTyMSy94KsYv4iLCLsVxkM-qQYjI87YB_qG1ducQHnc3BWsdHyHHtpvpCQjsacogj_NgSMm5cM6m4g7oBOZtRifYfXoe-HSwZ4G/s400/25.gif" alt="" id="BLOGGER_PHOTO_ID_5371186192849740674" border="0" /><br /><span style="color: rgb(255, 255, 255);">______________________________________</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHKCiseQSAfP-hTW1jsKnzII2fm1Ai7PBEyF558I2srYxXP_QbOZhtxNIU4DReZVzco-QwwoWFSCoTJQhG82g1KiXZw_NR54HfOZbKjJXKKJjpTqJCpa6z4ehezUbI39O9arfeGbiXvp4C/s400/26.gif" alt="" id="BLOGGER_PHOTO_ID_5371186184478898946" border="0" /></div></div></td></tr><tr><td valign="top">2. </td><td>Kita gambarkan kembali soal nomor 2.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHETnVmKo0fDCyf-h60mwgfIUj83l7AIkL4i4wz3mDNuBEqjQqIOWi16VcoBiW8hEqspbtYmy9NqRhwaXMqdo4GBvc1FLBSqmRZXuL7MUk-7X-RqcOX5NLA_DNjaSU1fGdza5eaFntlV2T/s1600-h/jawab2.jpg"><img style="cursor: pointer; width: 400px; height: 220px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHETnVmKo0fDCyf-h60mwgfIUj83l7AIkL4i4wz3mDNuBEqjQqIOWi16VcoBiW8hEqspbtYmy9NqRhwaXMqdo4GBvc1FLBSqmRZXuL7MUk-7X-RqcOX5NLA_DNjaSU1fGdza5eaFntlV2T/s400/jawab2.jpg" alt="" id="BLOGGER_PHOTO_ID_5371276164284225570" border="0" /></a><br /></div><br />Seperti diketahui di soal: <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh07zKzryGkkPBfZ71_EOKDNOBaXHDeI80_Hmn6W4gMsAQHdBCZ4ubpsX8-2fSxL5Y_vrkMRZiNDX7Sbg8I152Ul4qXDQb3Qx4lQbYmneJn2iv5Pe5DbDAuDhg3yqpDSI19pUMFCtm2Gq_q/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5371281411627740226" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiL0O5F_2uAm16cwv5CcIgpJM7FDQAnkLedV1elspEJZ4fB2UfU78i-sd00nZjsG2mtEfSS5hsVV6QTTUN1O5wdfRfJ1Jbf4SNKbQnucb2izPcQLMEmiGT53C-e4s8rbwhf4QNu6Q1ex-O4/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5371281180305398866" border="0" />.<br />Yang krusial di sini adalah kita harus membuat titik pusat lingkaran O. Maka, kasus ini akan menjadi sangat mudah.<br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVP0bKg8p4pmrHcf4ARIa3KqJsm40yXaeFBgTa5HQHt_XIjmXqn0FtDbN3A2e5Lj_j6_1BQ0UOURJ_3d5eWHXBRUmNJULzsK4whGkCWzNUkrJKXEpvsAGBwRHPKmihaLOVP53m-vsiGx5R/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5371281174067688562" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjy2X6HQpogk3KXoREUcwSCyuDyT7n0BQts22wcmUzZi7UzJbXfsr3wJkzeyN29P9jvqbSE2o425O5mb60hBmYqmFmI1huAEedoTSTTYOYm4YVZ7d6lEJfgpYMkr-fIITHZO_TnnoPb9sv_/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5371281168506248642" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7cu_L36piX0ZTx7BdsJ-TU2RZEXJ4Xgl0sjKTrgsBVCFYLR-Y2gnop17GzmhO1YkgdQ_YLFP7mrjpWm6f1sFQ7ndu_d6iM_q7tOBpu1s9y_fCUWLbOG7M7ZPzf-HB3nRIf83SDhkMDhoa/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5371281416512692882" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivBGEDOXhI667p9GTpd1b0vvaNMaX_hXgRBinkZHTQFSMPt3TFWMKjku_cOHAe-YikKzYaJhBydd6U8nTHmuttN3RLhpvKmpJKvsDYSr10JpWSgiGdzVCxEoxnZ803CWRSJ0xgo_IhPglB/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5371281152877314690" border="0" /><br /><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9E4ijg5_X1N84fNDjrb9knda_zITxqrmQuN5Y4ZqHdNPIgMf09tNeQhL3Q-vxpi6LPbrO-edQGmm9ngHf4d-7_ilKgPr7-5-BRZAKEa5mwSr5lVtMQ3tjy7kjvP8m8uGPbQY84laiFqVP/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5371286314398528610" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxhOtXNlE7IPV8rEJ3l7yliGkS_HquSKJ9wvstwVAdBq7kFBVMKb2Kj85KkMYIzyYFXWmOWrvPXgGe_dRYNa6jY4ENNJHs7WF7bEGMO9c4UCWCrQLJicPq8748VIdI07o9r24e0qEP0Q4Q/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5371286306803577602" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuCDdM9EFvXN3OSvkw_TGXPzv1nCOMeOnccKpks5P3H-emZWX8kYjIdf3erHdz0gzTIixOd3rk7591241gmHg7dV0BWMgXSt6uHGIUojyf59hJyDij99OfkW0gMPAsYCjJDq6QfFjO9oip/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5371286298376399138" border="0" /><br /><img style="vertical-align: -15pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrI9fMkyhz-EFxfSAQ2t-5JjhyCjCY3EMs2YBcJbtBiO0liK7LZy9tzeWgvvz0h9C51VrIizO8-RzQn0Rn7Mjcg0yXH3xcPB9ePEp_JdhsNYGXxGcUTMWRTcP3_VsaY6BFUqxYUhmhmxGs/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5371286131142176482" border="0" /><br /><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgFWpzW5cQ6Q1Ifjuz8rJwUtS8wYGwhhOIbNqAp0Eeaj7vRCwKLy5c5MbLXXUPzwMVRbiGJd8VacoH1XAauT8JJehd9aHGwfx6Kjj2CTifi0BgrUwI9WetouvjwUuvD5WeQydGv3tOs_qq/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5371286126553247922" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihVknuN8mpkm3BTXpdYYVb-bIH4Q_zkMHJipUJ5GDbyOUe1r41Kphy3_3o8odrHXqkb5j6pMnGSgJxmaIK0o8u7bwXZxXklcuADSPKh-Ids7EA4eL_JKIs0As0hLIM_rIVhv19DLZOcEHH/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5371286125069667186" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwSBuXLcahxk2XP47w7b_ELpJDh2d3hpxiUTJBi6_OozN4qgfegBif-hn0CV8nkjrUXwd0WFWvSf1yVmwl3rvodm65z0Ux8ZHHcXI7vHQRDj0BM0J3wmuaxv1GLCwsudXRL3DGv4z570jp/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5371286116540612962" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhH2J_bJ_-a01Ne56Yb7rnT26QvZafRAWXXOJBttTATOyBlyjHCPqK58fQbNwWN-tVtkuilIHnXQs2yf_aXbJm_J-IUBatF-0vblOChmGvibE3YYNMs0TAzMgmiP6zAmFdI_VI2QvwW5LfQ/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5371286112911929346" border="0" /><br /></div></td></tr><tr><td valign="top">3. </td><td>Soal ini mirip dengan dua soal sebelumnya.<br />Pertama-tama, kita gambar ulang.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1xG8w1gmppL8syFL_30jEFO6mWjbTmJPVpOo-D6xLuhq00O4skNCMRCiwQUFGBUcT6KIZGpF1n8BInGSvAFvPX87WCjVGfreem8nW76tKu3YYq0ID4OMgyBpxmCGbab9G_JpAKxgkt3BK/s1600-h/jawab3.jpg"><img style="cursor: pointer; width: 400px; height: 219px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1xG8w1gmppL8syFL_30jEFO6mWjbTmJPVpOo-D6xLuhq00O4skNCMRCiwQUFGBUcT6KIZGpF1n8BInGSvAFvPX87WCjVGfreem8nW76tKu3YYq0ID4OMgyBpxmCGbab9G_JpAKxgkt3BK/s400/jawab3.jpg" alt="" id="BLOGGER_PHOTO_ID_5371288503114283186" border="0" /></a><br /></div>Langsung saja kita ke inti penyelesaian.<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEil1ia29UAuUuil5Lu2ptWvy-rQU25rB_B7KUP6bRadPuSeAGMMw5rUS5xBThRrVsMH7lPkGzO9_KdEQoeJCJiGTqQjOYNe-wPbSjU7bkcmx_LOqWGeFlCbDcJesfgjTIQtwnesJ-FGcjGF/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5371308965753538194" border="0" /><br /></div><div style="text-align: center;"><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLGNVB7Ei0dVqRs_g4r-TSn42XFGNvPumFgH6PBgt4JiW6M_YeXiSrceT_3oJM9ZJ9ouBNrRcmGvtCm8-w3-Ov5_zcsPGfFts_mgO5M5pQLaMLvZtwcuKjaj_goLlXfADLf19p3yTpgW2l/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5371308889192028242" border="0" /><br /><img style="vertical-align: -7pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEin8Zcp2p9v-k35HaZqKJn8xMs5WvzPeritTioG2_Cu1AupxSxfLqMmJjnCTIW7WZPs0AFjzriYymxc27URLMQMDfKTkXVSB2blSlU0FXZwsIC_jXeIFCi7zkoRwHaGq6UOGcqnQlXpr9DX/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5371308880936635234" border="0" /><br /></div>Karena <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_OiizCN62ATvgGt9fiuuWRoq6p4ZyQQdXh7nEkFyJ03UE2t5eAAkp41w3O89WDi2YjIn3oxUZptCt4fbzvTFO6RiT9-KYd1or8aPYt6Yix5iTN8ECXsHBe0ccHHGSq_LU9QA6U6MzjJqL/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5371308869083954402" border="0" />, maka kita misalkan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZ6Bf70Bc_WhkV-AOG9lXiA5ln_Wm99EDkssp1lFZt9SSqqGwAj_C5eRewSrkIqkXQfWRuk9O1gVR1GOPmu-0aglGO4vLYH7mfwp_itxU0kizQCj5vmkX1JzbBXuUM_7hJiCYMEvzuH_3Z/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5371308865014372674" border="0" /> dan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgkzKfud__c_YlbMeR7Se2ZMJD7PvV6S3g39RJzPlR-N2m0eM_LaSBiKFxICR1GKivERIeigjJ2RhiFQAEgvQAFVnaiQ4uBbOfrxl4F_shsQ3uJsUuAPjaMICYdomffXq9ploPgWBGH2aN/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5371308861757563058" border="0" />..<br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgP7kWQh4PO6ykoGTe16oEImnaYzDoM9mZ2dBLj7T5gdTJHr7svibD6mb2ET6QyUpjFP8mLk7XmW9gamHA3I0KKyZ6iM4NRsDdKZFlQc5y-dN0f1-L32q1haBQOFy9s0y62KjonL53BWOUw/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5371308745882663538" border="0" /><br /></div>kuadratkan<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwQ1NRx5kB7Bv8EheNX11WBt6meGR17FAdRHtHB2zSYEgaFIqagfOIRfMJv_kpiX3w-zRu4OCPtGGG5KVSP3tRT_s2X6A-DaxdLVdO-fic6MlO8CabixoZeehStVb0zYAz_yYhZW3U1rL0/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5371308739525648530" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg06qNnxtKDiau5ZKz8OQrcu18nOAV2v-Rs9TsbQstu030rHvB7fbzaidQlGwjhGdkg5TV7oh3X9HIpGZoj16iH8yEvZqeZ6h7pw-JxL5gcSG7EUvOqf3Gwki3eyNnJXcawTa94a9LfyWe0/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5371308732873735346" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhA9Ik8LH3ajsEFZzqBYxezRfvwiBdQerxEvWzA5oZE2CVykQifm-QYpwi_0WGAD0U9pSEp0LqCOis5lKh097PNDrNYLQbXxKAg7aoMfFXCh3dh9DdHY1d6AJDRFd1ArHf9p3EO-pukJeRQ/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5371308726753788290" border="0" /><br /></div>Kuadratkan, lalu bagi dengan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq9HcDfI2xtWWmcVnJA3j6M5uQ8lRHv-kt1piDhXp67bp0s72Z00-BPM43BtodlifSZK2D6UUljLBiRvPi3lERhTZZAV22rg-xsD2IibuWi-vla8dxmUc7z_Qq71OTm8MDOC730VdV06DO/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5371308721033854802" border="0" />.<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTXMpTWdJq28cYqM9FCG3b-kQlEXdTO4YrVBPygkPlFb9Dgq-PcWq_bq5QdCrIC68rT-U7hLgWc_2GvR-ixX9NJQ89TRwEYuxxq7m1AQ5AKUcn40kpHE1kg2Y8R6-nigIT68uwN_eURQft/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5371308601408517026" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6h0Cba8qiECuE8mbogLQAjhSq33uTY9qeEsMgIROCW-GAcxeKz_0JPsxt3u9bnU7B-pVvsuYVtpzg9mJn9oYHckg39H6YQMThjzTvVKv3_APUkaStsqAvJfr8uQjza6Cx7-gpP9APdx05/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5371308590915409602" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbzAKUdv-uAszbzkwqxxIDtmNkn3DsZqJtQ-L6obFaIjB0LhLFxF3QKG-uJB2snJD05vx34OudEQm4IWqxybNL7wO7Exixx5gwaQ2oIpspfhqGkE8ed2_x889PEcPI00hoiW7RHeTe2jKg/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5371308585445420690" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdLiTnj-JxIvRJq5Ln3Oi9uyBHu94kY__V_MEGG4mbNwT7Gl0HBaIcq8XIFJIWxCdLlBfE37GFWUGH9Mk3ZrcIdKgLv637QGgiRNr8zgbr3_4dHyWbMGpf6YqaMIRNSVJuyXuYgB9wVLIg/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5371308578983116866" border="0" /><br /></div>Pilih <img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqHxOcrnO8VirwT-61LwesPjCY35fyipzE-6AnpxrK2yX5BcMsR3KJh3LfF5JozWm0tOBceoDwHdZt534QvxD79pmMBnIuwoT_TBvOp7wC4Hb0UTREDJXyNlP1NQIQrufctMWGJvAySHhs/s400/16.gif" alt="" id="BLOGGER_PHOTO_ID_5371308571082114626" border="0" /> karena <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgp2nUx3wlGPpTMr1YgH3IfGkj0wmWohsk-2FgQvxqg9j45EkX4TE-9dlrVMZE5tGVn0tGCXF4d03ulo4JgXn1_GugzBK_ymQFyPzCQ3ivi5CgQp0LFc6po7zlzkQdvd9zf6b5JRFWeRXe6/s400/17.gif" alt="" id="BLOGGER_PHOTO_ID_5371308432521789378" border="0" /> harus positif.<br /><br />Maka, luas yang diarsir <img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhB4ckZ3crVjFejQwF7BFjuPIFkSbqLpsNdOcIt7ylbyZU2O8xMtSZglYW4kT2SNQ6QSrzD2X-mmo02o076fMvPlPqcWBg1ZM4O5CbEPsoAtAFP8-hXjVaIAPqdoNUGl8C-BK7rJtWVNcZw/s400/18.gif" alt="" id="BLOGGER_PHOTO_ID_5371308421882170194" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________________</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsl5werEsLYpKPAB9jBIIRTf7w55r3yFpPbWL6mxnhoIEx2XDWi5H69JFZdqjmCJXGKnCtwPelQGwwdnfZDreoZpWBu5Vs2zfGCggFWO47ikd041TxOVh3WpUxGaSaVMCDgvjhjtPph34G/s400/19.gif" alt="" id="BLOGGER_PHOTO_ID_5371308419960775570" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________________</span><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJrurhuoAh7AlQVZAFvaYhv_ChW6Wz4dm0dlME05i4fj61u7y-PuvqqQv0kipnpDs1UkfmlcBE3Hm-lUUI5g5t_aTW6T1Z3auss1WneRNVQuQ4JeUnVg9FGgIrG959Bur1bMBh-1H9B3vf/s400/20.gif" alt="" id="BLOGGER_PHOTO_ID_5371308412186778194" border="0" /><br /><span style="color: rgb(255, 255, 255);">_____________________</span><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgC98tnY9eVEBjUMaRiLgk6ScwZFi5tcgJtb8JtP7AzxnCS8m4FnRsSy2v28w3Mf_OzO93buEyH0NA8vTVNTpIKHAHl6i3JgZkTPfoayGmsiQlB9cH_N7bvyQMPef6qcdGfQdnuMRM5ZZsH/s400/21.gif" alt="" id="BLOGGER_PHOTO_ID_5371308405546172866" border="0" /> cm<sup>2</sup><br /></td></tr><tr><td valign="top">4. </td><td>Tidak jauh berbeda dengan soal-soal sebelumnya..<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGxycdzfruukdtjtvJiGNiHPCVxdyIhK2LmLGhu0pcTxSFSLwBICV4uuAh4ptFF5UhIJ7LFv4xaohAPpzGZWOi57dFg-t-_stbvmDRwV35e0D_MaxVawDu9D-Ov06XoV3AiM1cyGCXVfFO/s1600-h/jawab4.jpg"><img style="cursor: pointer; width: 400px; height: 225px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhGxycdzfruukdtjtvJiGNiHPCVxdyIhK2LmLGhu0pcTxSFSLwBICV4uuAh4ptFF5UhIJ7LFv4xaohAPpzGZWOi57dFg-t-_stbvmDRwV35e0D_MaxVawDu9D-Ov06XoV3AiM1cyGCXVfFO/s400/jawab4.jpg" alt="" id="BLOGGER_PHOTO_ID_5371313900243388658" border="0" /></a></div>Perhatikan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiy_phdy7Y1coAdKfOskTOmj5T8KvwId4o_TGyV1AggBgtpI1yrqkj44dicDn16Qztanf4sbN2XkQfGh1Z6x0LkNPjH8MjJbfTVV2ccRJaZiESkjHD4iZHccWOasbmItAJKu53UDDXsr5Gr/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5371319101615916978" border="0" /><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFgWWao0pCkaro-YXDgDTJCdI7cl3Xx7zExE5x8EFY_4B4JsCP1QXKMBoCSfy4Rxm37_cQNTlFBYIV5P44MrmFyeJ4jTIXZAYvmcOBpYgLno1eX0pGFbJJmsfM5HfYEn4lWM5uprAgzWV0/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5371319092164171810" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2kLYyyk01oXB4bw12Ra_A0arHEC5-0gugkoGDo7RO3CZrlycMUZwIAsNYqkug7xLQTdBuxJQ_G9a1H7lnd1-sCk7L5O9VYcsZlLjmGs_sKnBBQEek3T4N9-cwoWF6Xu9qcU1JQPoCoiV7/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5371319084353022210" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOrgq8vV2C-Yklf2zYoKwkB9Bmg-Jfa2aZ6uWBkR-Bfto6RSEb16VSGPSSRmkLz-_dwvvUgCRLWoJCIUdJVvChMPJj2SHFrJz12C_MPOl0u_C7niytiYoCDS7HB4j8K68b66xLxoew4h3d/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5371319081220633634" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVLVflnKat605PXCCv-USj5KtDs1Vh1jKO_drykYHJipg7K_V_c5v5h-ptZUJdxNBrxdE48N__llaFKM61CW0t7bB4dh_d8uOiI0vNObUGVXhxgSMQg5wKcz9zB8hDHeoW9Ya1S8hcE8zo/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5371319072882072450" border="0" /><br /></div>Perhatikan <img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq6F60XKpAF8bLAxhA8cj8OqLVGh6jnrLUxG-QcgbgaXgo-YXqbsdt6CA8YSy4G9HFMCBU-I7LB8GrIWQwz2gJOdxKYsXigFRdQI6YqGap5KPOZCJPvPpJAnWh5M75JjeutJjSiJzvhxzM/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5371318942894118402" border="0" /><br /><div style="text-align: center;"><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHDTN6aXLXD6AmNXHXLR_SNi-nJfRXuzjFkQj7FEQLP2t2_sdmeLv2boakkigARzUmnMcFaChQiwRKf_R0IKQ4syz_MS6DycONcspMDh56W4ZcIgh5l0J5t3gWPAfiWqoWxoqbNx-6dxuB/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5371318935732121858" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTgBmVPTPtBkwsq0vqNOQm8Kxtcl8d-FlsMQvH3g5tvweEv91Zc6tPLN5IRYWkI7ncgrHao3XID1zVEI_GFfm-s7C_isKux41dko06KrjHRuyTZTziz9dMwMbu1PgI8pUi2q50kbIhqve-/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5371318929484208834" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiG8TiiePh3lujmyy4TURRYpYC2YX867Haa2mAIy-f9j9G8WuyQiJre9acOGigwIWE4L_NWo_MSGyXZjDJmzXUm-d3uBfMHAxTUfh5zlzqgTsFOdOBSL7e8tGcfm3S7BnV-0ZqVdhhbklJ1/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5371318926107587426" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_SKKwdMKJ-hH_cih0-bjmlqzlYQzqrt6nLeRWFzgWZnlcYbzQwfCI15Ec1kSVbGV-Stl7fJTyg8WKzGXRzGu6i6x49RKOCkqTC9dEfEHPmjG9nidaOatKf72GfW_22SWnjUII0AsIrGzO/s400/15.gif" alt="" id="BLOGGER_PHOTO_ID_5371319977454399810" border="0" /><br /></div>Substitusikan pers (i) ke pers (ii)<br /><div style="text-align: center;"><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh9GgiFvUsy3aopuUa6_HD77DH6ui5O0Fy5TAFzZKoo9cxMToqZaU96DDiSPgT9_28ME450A5UBuWJZZuhcBh5FcbgYYRTwlb99eaFJgwz9wXvSA5g0BQRiA71m-CrETX2_fOEFyoeamJ92/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5371318765998453330" border="0" /><br /><img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQwXbr88t0sj_ySI70TOL53QG61phfhiu7EWWnYZxe5L5tmaxMwqA0jLRc52YBvVsE0OTs6aSUdYuyPU0TAK8vAEPE3cl9wOXUl76EHhrCgLuaEFxlFW2oqkHQd7kYq0mqWy6a2BdnNcog/s400/12.gif" alt="" id="BLOGGER_PHOTO_ID_5371318763597889778" border="0" /><br /><img style="vertical-align: -3pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-Q_OeEL81LUH6vKiTtiDYF4hwVXKk9Crdmo251lGxCjllcNA6SMioV2icgSUSIIqRnCTAB6G_U7TdK_uy6Bah7WJcQfCI3fjVv_xFLnB7TfT1DVSfRt9H6-IzZralZ1VVek78dXzCdYqi/s400/13.gif" alt="" id="BLOGGER_PHOTO_ID_5371318758319282610" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifmzSXmv4T13vEC7esf7wPHkmbnQ7MaStYXWM8NinUsBWqjxXy2kzY89KiSOptN6jbCe1mz4JEWIMIOFvXv1kVU2zuiQ8GvbJpd3le7P6YvasbNzLeNM2bDMmJEkgftqAy5l2Zwuck4-RM/s400/14.gif" alt="" id="BLOGGER_PHOTO_ID_5371318747444979474" border="0" /></div></td></tr></tbody></table><br />=======================================================================<br /><div style="text-align: justify;">Dapat kita lihat bahwa soal-soal tersebut sekilas memang berbeda, namun dikerjakan dengan cara yang serupa.. Soal mengenai lingkaran di atas juga sering keluar dalam seleksi awal olimpiade, dan sering menghabiskan waktu bagi peserta yang belum pernah mengerjakan sebelumnya.<br /><br />Jadi, jika kalian sudah mengetahui model-model soal semacam ini dan menemukannya di soal pada awal seleksi olimpiade, anggap saja sebagai soal bonus. :)<br /></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);"><span style="font-weight: bold;">Sumber:</span><br />1. Buku "Kumpulan Soal Unik Matematika" oleh Tobi Moektijono.<br />2. Buku "Olimpiade Matematika untuk SMU" oleh Suwah Sembiring.<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com2tag:blogger.com,1999:blog-8125318493233557109.post-50208037212976300852009-08-16T18:03:00.032+07:002009-08-17T14:47:34.875+07:00Ada yang Salah di Nomor 13<div style="text-align: justify;">Pada buku "Kumpulan Soal Unik Matematika" karya Tobi Moektijono cetakan pertama yang diterbitkan oleh Grasindo pada soal nomor 13 halaman 15 terdapat soal seperti di bawah.<br /></div><br /><div style="text-align: center;">Berapa perbandingan jari-jari lingkaran A dan jari-jari lingkaran B?<br /></div><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihKfrmX6s11kf0pDxRF4lxFaImLTXkZWcVMdYFiT96H-87FznkuJR-oEpTlEfUhoyvkev2tV-QqDhQdJ5FIByyJyFQrdxXHB2JUCTT_BS1gylRAXvecYgWn_nVb7FCW6wz5Pu3VaA3_LEH/s1600-h/lingkaran3.JPG"><img style="cursor: pointer; width: 400px; height: 139px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihKfrmX6s11kf0pDxRF4lxFaImLTXkZWcVMdYFiT96H-87FznkuJR-oEpTlEfUhoyvkev2tV-QqDhQdJ5FIByyJyFQrdxXHB2JUCTT_BS1gylRAXvecYgWn_nVb7FCW6wz5Pu3VaA3_LEH/s400/lingkaran3.JPG" alt="" id="BLOGGER_PHOTO_ID_5370413609481904946" border="0" /></a><br /><div style="text-align: left;">Saya berusaha mengerjakannya, namun merasa kaget dengan penyelesaian yang diberikan di halaman belakang..</div></div><span class="fullpost"><br />=======================================================================<br /><div style="text-align: center;"><span style="font-weight: bold;">Apa yang Salah?</span><br /></div>Berikut solusi yang diberikan Tobi pada halaman 98.<br /><br /><div style="border: 4px solid rgb(255, 194, 89); padding: 5px; background: rgb(255, 255, 255) none repeat scroll 0% 0%; margin-bottom: 5px; margin-left: 0px; margin-right: 0px; color: rgb(0, 0, 0); -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; text-align: justify;">Untuk menjawab soal nomor 13 dibutuhkan rumus berikut.<table align="center" border="0"><tbody><tr><td valign="top"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEid9OXH7jlIEy65zKX6himDPJCI3ssxm228WehPIJPODUriqwqV3oyZZSj3GDKFcGc6XJlWQqoce_jVsjWELA8DortrYteCrG9i7ZAsbBT-kTvqeMiZbZorcwRXZwATbSMBCBN0H4RX5zG2/s1600-h/rumus1.JPG"><img style="cursor: pointer; width: 214px; height: 148px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEid9OXH7jlIEy65zKX6himDPJCI3ssxm228WehPIJPODUriqwqV3oyZZSj3GDKFcGc6XJlWQqoce_jVsjWELA8DortrYteCrG9i7ZAsbBT-kTvqeMiZbZorcwRXZwATbSMBCBN0H4RX5zG2/s400/rumus1.JPG" alt="" id="BLOGGER_PHOTO_ID_5370522505364865970" border="0" /></a> </td><td valign="top"><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm1ju2L4NYTjIxSgWFIps0V51Zb_StaymuW5QDOZnSeT_aAT_udz-JnX3ql6VIo2SfQxpINzOa4DKoFpHXWIOmdymnrcjYf3-grP0MfMV5ndqn9912XLGSOt6_wQanOstyC7UIQK7bifhe/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5370523780801037618" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwuLTn0fjL8BdMUBgxPu5lAc_FJmd2w0hrZF_sW5GDlQ0qIaDCATBotRcZ-RxumSEHXj2GaOsWA_7JXDeuVyW6I1ZIQuu57rXo4BDv4CWubr-DKr6Hz8Isi18fS1E7hysvgkJ_TSs7v0rd/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5370523701833252258" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihoXi7zzUp0ulbz_DfgKjGi1pF1ZQUckHVSOcz3jiRBcMlU6kRaTrJIH49-bqK3_j0xAUwK2mJfRHq5LjRahpfZi8WJ38JosOQ020CigeEdnIEGRyfua19UvK58wHMSDNhJ7CqW_vnUkyY/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5370523698431014850" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS3k9Wz-7zpG0l9ra9TOmPg0tAP_YEnyvHDR4RRbsi3ObN_ZAHbBEdaJhBwaTOszT15KzgWWV9EsBdDjfuRm4KgKEmto7Qp9qHUZePUfSS5SfwZKYkbVL1037WrNg-AZDgZaLxMArsvTwG/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5370523688906097570" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMMVGUgNYP59WtiNbYCOblSHYGyIuu0M08yWly40JUyrhVVyzfgHoxqhqm7iCsVli3l8ZftHYvFAKR5Swq1QWTTHawPc1RPAUZQlvYXJmclaRzPF7YSLLVTF9WlsT4-0DbTLAvBoECOEp-/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5370523687167344450" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjCqvIhX2vTdDo_IEgqgm-hS6-gbCyc4fqtdqaJhyphenhyphenou1VNn9YwgLWWgfnNQ2slILRTRQ7i7sJv92Yhs3i_GbBDH5PiYgG0KkKRQFFQYd8tQob-4RWhPaR468sE0ecbtzlNI3LMZkXeVRulB/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5370523675168492002" border="0" /></td></tr></tbody></table><div style="text-align: center;"><img style="cursor: pointer; width: 550px; height: 258px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5Ls3VoUWqLqHIaxGjjGqj0UdY20GRW_9zQvfSeIogk7gyvbwAxhlhu5di0SYBLnzzpDbcCmhlvzt_Lx5iOh040sOVm3e_TkVbrrCoz9jfM1XpKIYA3YZfDyPXNBOHdz8_gtDUSdQxTS02/s1600/lingkaran2.JPG" alt="" id="BLOGGER_PHOTO_ID_5370536053577450370" border="0" /></div>Misal: <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAOaOnY3Ug14OICD3CBq5aF-adFvmi71X6qvekCSXQ9RMVu-6EBs5d94FnPrXRPuX5GvksrS0SsDbOY-YPpa6bmgry6JXqpYTXsP_hkmqkN5ZzrRV9IH1j0xE-JVDWR1yvcviycEh_lBFB/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5370567524715611874" border="0" />, maka<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj1orb15uDjjA84up7lVCE8xcfQwpHbg9-hPNQUrg3HhZOxNP4XJQ4AsOL_a9ggDKqoxBMMWwM_Ub_xKDDQOvSGOtHweipKwX-fGJ24HYAR1JZkQ2zYBmtinVAG0SdC5pUBuHIKCUVImrlP/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5370534054952472146" border="0" /> dan <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrlEPzY5ASQhySJ79eFN52PgVUuEk9UdOAQaP7wd6gs7Vs68SL8d6Ki1NuCZs-SEyBUXbi0a_Y8W2L1IrAI9AhyrByZR8D4p1d8AGwEOs6Bvq4rg6ae3ar8-QIAZPxqnTj9O6PjmU2N8qP/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5370534049700412146" border="0" />.<br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZOUDMSm9wXXd6B-qkayPGdzVpt_YBpdSrPsbsIPR_Q2CaR0pjWwCIJaFDoX6T5aF7itGdcEL0SXTK1PE4rPyzlT_v836CEI7MriLa8pOeQ0V7CfIv-OIRvViyuggO3DKLBs6HZSOxDyxB/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5370534040181477698" border="0" /> dan <img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwkShH-1rA8YKjq7scS96v-9tPwIwNQUsspNG9Mff35CM1WQBY7ZzldheeI7jGYKIxv8foq5_tqlHzKDwBn6SFohSFZdMj8xv_dtKtaxcskbUw2IKLDLltE_2ChWnFcl8h-jNDVyeCxcDB/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5370534013733522146" border="0" />.<br /><br /><table border="0"><tbody><tr><td valign="top">Perhatikan segitigaTKA dan RPT<span style="color: rgb(255, 255, 255);">_________</span> </td><td>Perhatikan segitigaLBU dan RPU</td></tr><tr><td valign="top"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZ94MIqFKpWUaj6cSo0nQmHVTyY3arluLlYhl_gNJJ5MgBxM_9lXtpKZT1PbJaYRR04olFkvBQqw4CnjDyULKSfkqwzLQ0mwaraquEA8Y_X5_GzDhOLniJbBtEIwDBbh57kB_boPfz3M4M/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5370538754593544386" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj59WETAcLxQ5TpQR_QnEY1-frrqtIr6CpItFdqfI-G4GAHjiwxWwjc6gyriTu6oZN96yS01J4Wetq1p4rT5Cc-ko5XOtGeihl28tm_fCuf8dGA5A66y4Ap3hW1TAGMaS42PbzLi1emx_zb/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5370538748576039666" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNTWYUZrEcFIwXhn7vZHUgmP5A4Pdr4JLWAFcv9dlLS5Xv9dPKA9mJLMNFtaZY1KkRaJRtC_DDai_oxGC23L8uJW-L8KOBhAS7JmqTK_RSdYMKnCAYLxVjy4EmqZoBp91Bo2zqDzGKD-M7/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5370538741921860514" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh2zYVA4jfhGC-g5mufokZ3FHsFFr5SVDExYO0R73v_9Yf7OTm1XSPcBDYcjPPbxSAng_nmOJ9-62ab0O_E2srQp7GX_dtJfCxuf_wkaA7cSBXi3buTm9Qa05yxPUgVpARRh22MYf_6n-H6/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5370538733461845154" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKQA5xxBVKMuHB6F7rkbjtsBv2Xoh2DlXb5LGZDutbWwyV0HwRZCt09irDgQQWNnrxZwG_TgTlp3JCSZr8BWX6bSsvQIcaZV1T_zdA0fGp8VF1oy_SlBthGZrOUXaZ2rzqxtCKXbVqcmpt/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5370538618972832338" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgS60wwJ_1FTPjE_OJtQAjceGyqexwNyLDVvgRkSsK6rYTszOywiMI0nr-zn7adt42yfX2k0WUyThI_Zad3oQlBKrQGqB0-69_puO-mKCNvV_o-Fzcc-NCIB7124666eG34eqGhObEYdtRv/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5370538610338629250" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0DKMk5eSnJkToLtopM61GdBlTTNIJxuJggT_7d46hN9ZzuHEFpdxGRmO35kK9AkjMjrsLHWw-TwTg1SM-PfgmkkngYaPNOMpE1-tu6yqdr5Dg3qrvnggICPpRwa62F5Tohy5ds0M8AKnB/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5370538606220684706" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiedJcxuHK6wUB9L-3htgbM7U2LtCWg-Z_6pbDz5hNRuR7LxduSzK5k5u2aNhwn6Ml34qI0GalUlFUkTJCKCLdu4Ac7x_F7TGf7hNSuKvf1nCuz-fKI_hACp_EO4cUdZIlVqE9-OON8n4Xs/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5370538595774921266" border="0" /><br />Karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBZzyoKwHFjozTOvFyoQDTJWsggl1EEk9C4Qj9H9dMrUKqh1RGqZJgxn_k1ngeA1Yp8utEybjQ0D4PIU-q6Lypn0YC9rQaL97l46UdB2gTFLEnQuvGaGavsbi6mRDmqsJ4sR71ujYmwsU4/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5370538588857942898" border="0" /></td><td valign="top"><img style="vertical-align: -13pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgi63Fym5UDZZJxBqPxOk4JffcQ57p4ZC23qU2SXDktNCXvLKKRZmvTPqJpBw4QWrtgpWb-7cDtNhb2Ne-aWwRf9tknU-9Ew4lUkgY7wIZ0_tXMCDyspPz4LoDxoNfx1nHKAOlNqG6uMd4b/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5370558678701741634" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiUUrbLaWLFo7ihDiruHQnjqb-2GMc4AAw0bgYVkPeI1ols7n_9dIrIIv0_ace4s4WvpeK8uD5gmA-OXBNEUJjORWZnzd9WNNZ2i7uF7imGff8f64zn8BSWg0Rz6r05PYB_ZVLX6i33Ar1h/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5370558667178283266" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhetjtPjCzf_Igf9jLOsAasoVr3uA7D-8hPHKZMXNGFmMYluYG5vNIE7BJbUhxrOFOoF-FBfCrxbiR8V-7bdaaZ8cgaKUmu1ZzpH-eyDqXpgZWe3kwuIdUAJOJmBuufv898uzaRaavhWSOg/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5370558653736265058" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0MkRQERVUPv2KLWy1y8DJrhnSpuKf8olzGil2GpL-kU6KAm7Idry-ee9UevpByDyQwFDcl4cw0uTKOwOoXmOU4ceyshmujtDCx-OtUxSD2COIV9hUgYBvRnUBOu9t6mCeB4KniHrOln23/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5370558648023525554" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigFpBBlUASKutrPdMpcusckhF155QK9-GZr5gUqJQ8Pfu6_oJdmM1bbrw5rrTy4LI8OhTOORmo8_6cVGXph9WTTKUE7rXbZaYtX9EsvZrK_xXQbdlmsrLgkLY7Mw8obKqYlKeMFDSusJL_/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5370558534565395730" border="0" /><br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwRqLEyfDpMjNd9SnPp5U3iWg8HIOlMDq0W7Bi_FNy3GWskzU7IJX5fqsKcPY70h1b8ch0Uj6pFSk58a_nioAqr7M8blIxYXBVlLd9IXD8VDPoC5quA3F5tz2qaA7frYulnA4tRAgtvryv/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5370558527625245138" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgcA2Pzhtlcnj5cVb0f97p6rRadrOQ2aQ2FVOsLxKHUxw0pzY36h6yyD25x9ik7xvkJLVf7IRVdejDlYrwKK2B0JhAsBsfQEcbsO6KPpm7Yl4ATQl_QpnjCTzHDlux80tokFgvyfOwzo2P/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5370558522914116706" border="0" /><br /><img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEisRICxxlyJq2-MvaBq_Qon5TwmZg4rLt-8crwK5omIy9-8D3ugE_mQrnP-fKmrlHri-Qw5A1SRd39iF11xlEmS2zWv_5ZbW9HYyBEeuDpNDCQ7NuSmwJ9tuhIrJMWZwCQ6KzfmRPA-Gb1A/s400/9.gif" alt="" id="BLOGGER_PHOTO_ID_5370558493666067730" border="0" /> karena <img style="vertical-align: -4pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtJFCTF8q9mgRe25NBPdc9JOtbe44XprqvmooubO7iE2jT3hg1graA7GMntrWulEJuvwBcuVQ_j0_HCNpqCcOSE44Clz2C4q5TTmaO_oKNiFqKCrb_vHRWBTAMfU9EXNHbWLAJeRKVMA8B/s400/8.gif" alt="" id="BLOGGER_PHOTO_ID_5370558512203444578" border="0" /></td></tr></tbody></table><br />Jadi, <img style="vertical-align: -12pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4v7Lw4b2jYx7O4c2FhAfL9OimdEPwDbaUz11wgBn7WR0S43k7phgSGYzGLLFrhRwjHrjNOW2kEZVp7d_dSg9pIb1A7E_jLKFu7XOLA0CvBjQMFXVKI3qKbiSQGWoZurptbNc_pTGGASKz/s400/10.gif" alt="" id="BLOGGER_PHOTO_ID_5370559578370873154" border="0" /><br /><span style="color: rgb(255, 255, 255);">____</span><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwnXuydS7uSs2G-5hshYlOBTfT-HxMWvrQze164xfNw4eZ7vyXgn3zlujwD1-UEo7_vnIb133tVfX5oiGdHZx4WZLiWikqpLXcl-iuGC5QZBd4In66cTlYI3MLxGpiYEEEYIvOeqA93nco/s400/11.gif" alt="" id="BLOGGER_PHOTO_ID_5370559576212209826" border="0" /></div><br /><div style="text-align: justify;">Bisakah kalian melihat adanya kesalahan pada solusi di atas.?<br /><br />Kelihatannya memang sempurna.. Namun, sesungguhnya kesalahan terletak di awal pengerjaan, yaitu ketika menganggap <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgAOaOnY3Ug14OICD3CBq5aF-adFvmi71X6qvekCSXQ9RMVu-6EBs5d94FnPrXRPuX5GvksrS0SsDbOY-YPpa6bmgry6JXqpYTXsP_hkmqkN5ZzrRV9IH1j0xE-JVDWR1yvcviycEh_lBFB/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5370567524715611874" border="0" /> dan garis TP melalui titik A. Bisakah ini dibuktikan kebenarannya? Apakah benar garis PU berpotongan di pusat lingkaran B? Atau dengan kata lain, benarkah garis BU berpotongan di titik P dimana P pasti membuat <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipqoXjDjTSyGCN53plgP9XmzA9NZ2ncC4Al_DLlLx0vElxmImHk1I2vZsvO89CZ3rhj55ddYbKgRT1uc5cRoM5INWzb0MWHDQl7sUaZJ7eHkTa1Pv4IPrjtfXy14MmP8ymXGt04NtJ8TXS/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5370567534341810034" border="0" />.</div><br />Mari kita cek.<br />Lihat lingkaran dengan pusat A.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhErJO87ObLwV_NA2E5pCjcrb2If4I4lL-jxXUllM64WdRxFsr_1U-WthhIdl58BCrGlYeKRiIoz3awqhXvpChFbb53H7L_3PAa4bhbDtCk9L3MBKHbrNmuiE4sUk2A9gsj68xfja1vArQL/s1600-h/lingkaran1.JPG"><img style="cursor: pointer; width: 177px; height: 115px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhErJO87ObLwV_NA2E5pCjcrb2If4I4lL-jxXUllM64WdRxFsr_1U-WthhIdl58BCrGlYeKRiIoz3awqhXvpChFbb53H7L_3PAa4bhbDtCk9L3MBKHbrNmuiE4sUk2A9gsj68xfja1vArQL/s400/lingkaran1.JPG" alt="" id="BLOGGER_PHOTO_ID_5370563736627797586" border="0" /></a></div>Karena segitiga TMA dan TKA kongruen, artinya garis TA adalah garis bagi.<br /><br />Sekarang, kita anggap bahwa TP adalah suatu garis yang melalui titik A.<br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOPbzhm-BuSoHYBPakCw9_sBZd_ZXSw7955nOyk4YGm0HDfaRjyFgo06AoYtqGvMjgSd5PssuzAVgHpnj_jZTzKiUEAXIOYFv0lsEoHT15KUqLk6CTeCy5t7_Js4jYj-aU_X7P0sQkjVIi/s1600-h/lingkaran2.JPG"><img style="cursor: pointer; width: 217px; height: 187px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOPbzhm-BuSoHYBPakCw9_sBZd_ZXSw7955nOyk4YGm0HDfaRjyFgo06AoYtqGvMjgSd5PssuzAVgHpnj_jZTzKiUEAXIOYFv0lsEoHT15KUqLk6CTeCy5t7_Js4jYj-aU_X7P0sQkjVIi/s400/lingkaran2.JPG" alt="" id="BLOGGER_PHOTO_ID_5370565337389580066" border="0" /></a><br /></div>Kita cari panjang PR.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiMz13X538NmTcMAj51kL3tkoOjhaOCoJxs_3Nuc_tB79eWsBDrmalJwUXg7b-3uFqqmKri6rpDzOtlIWskcPzN2IRo_cyzGdOomL-I1t2sgkGdtccQPpn8RqrwxHK9vRbN7LZJItaPZScG/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5370566676692286642" border="0" /><br /><br />Kita cari panjang SP.<br /><img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3En4b01MSHWl0Dm_gqCrYQ5jW-kMEFgAhYrT1sKhOaLr_yVGGLXKwvaMnjig6_wIdQi5c-ztsIH92gMuDqQFnDCzErXOYHgTzuQXpITWu3ea60-2lrPTnnkKKS3GpOnASCl7_gOt_3Afh/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5370566673748223106" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgV9W_R5FZL5vMFHefU1GSfP5RkWjPbe_UsYkDFx1kUBX7mBMJRYCgB1hNYJjZRv3Um5qDAffswOcxgX5mgoX0ZYX6RsrTl0awsVSljN5VFV4lI3BSi4CvalHq92fhszceBwYkYl1q50csi/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5370566666202922466" border="0" /><br /><img style="vertical-align: -6pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxgszVDNHueREgCMrVG8Ndi4hWtPa-8iqrhN3Z8NpvZHNl31mbgrlOcx_Kri29sjE5s-NRUKTOouleGu7e7sP7Wm7zibqbksVNEJM3i8I0gVQdLDncbFhl13vmaUJqGiGIkNdSNaH9dmGo/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5370566658000080658" border="0" /><br /><br /><div style="text-align: justify;">Dari hasil yang kita peroleh di atas, kita tahu bahwa <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO3kB4UGctMeBn1Ql8cwGa263M7JdGCv6a2skJD7RRQ_SQ2BiWbkkDD08Jdi5VrTPSSAEH4Z2Zs9jqE4z-Ro07Yr0wgYr2YztOtDOrF3Q9ra0FHbRlQCTTebePcdp2ZKj9206m0q_h94en/s400/1.gif" alt="" id="BLOGGER_PHOTO_ID_5370571019182322530" border="0" /> tidak selalu sama panjang dengan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirmTAsZvQ3Wi8TLDhfKNfTQ_xMQhzR5YoEKcF34psQmtSrmVguYd7YAtUyZhArdUtHJP-f1tHE3mxyNfWvCxsN9cYh9Fex_gV8svLtxCjlPON3cmZDp64ibVCEcQ8SwUaPTOBpSWERgmlt/s400/2.gif" alt="" id="BLOGGER_PHOTO_ID_5370571012956559378" border="0" />. Untuk <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_RvD7w1PQvLKVQuz7eSbSjYwd8Csu2Fl42F2-ZXE3gkjhWkou5xb0NoENfbA67wWv6tmAWsuRsQd2ezy02AsZjUzCu0Y03lpiMN1k8DNupklH4KLWqzgDSODpuR4-_NUGbMuZKFlLCucg/s400/4.gif" alt="" id="BLOGGER_PHOTO_ID_5370570998403146738" border="0" /> atau <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigiuYVettBc7RlvVW8wINvNXk_WWzpyXdYwLwXGVj_U3rmvruuulG9fZvhToN_7KGJzDgSwRBLH3dCyeDs1qgD1CudB_XlbX9UiIq5owA_qVaw-R2ackghyphenhyphen3qkLDdCi7tbeI7_z7LilSbE/s400/5.gif" alt="" id="BLOGGER_PHOTO_ID_5370570992429162386" border="0" />, kita dapat mengecek dengan mudah bahwa <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3KhncjXzSN3ElrA1HkQanukS01dzbV8yEytv_P545-jO_fTUz4qaVu1LY36oDYMNBhEdi3Kcgs-bK1teouigAvrJK2_wwGhn1TvFsZbuaPmtHLkN0cTd5De2dYkLcCRuNPiJ7aYKwmk6P/s400/3.gif" alt="" id="BLOGGER_PHOTO_ID_5370571005237701938" border="0" />. Untuk sudut yang berbeda, maka panjang SP dan PR berbeda pula.<br /></div><br />Jadi, solusi di atas tidaklah tepat, kecuali kalau soalnya seperti ini:<br /><br /><div style="text-align: center;">Berapa perbandingan jari-jari lingkaran A dan jari-jari lingkaran B<br />jika diketahui <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-JNJUrT1ZRxOpndYx1HTRRP04puaW0zZyx-WlIHM_IaToj91AQkLjkE_VOJqWREuq04Wa8QAJRjk3hye_cYXJ_sn9ojYd-NVn46lN4q5A506avbWAIsqRzCnDLCWSrsZiPBb5HnXdlIsU/s400/6.gif" alt="" id="BLOGGER_PHOTO_ID_5370574435049061234" border="0" /> dan <img style="vertical-align: -5pt;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimF1-3e2P49ZQgw2xvEuQ9Q2aUaK_cX8aRvgHOrIkOiagVCl50goY7sZi_xA4xVDD9FFJ3QTq08YUBtGQBoHtu7Bq46Zk3yl-bPJSg64Ze5RR768b0OQxfO1cOZ7BCaE4Hdr1-l2oxSlgV/s400/7.gif" alt="" id="BLOGGER_PHOTO_ID_5370574426749180514" border="0" /><br /></div><br /><div style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvtQjUGNnr5i-ORTjOWDAgwPEn8h_9Ck7GeZIZpqR_kixeFNLDGR-LkL41Gtoe1SNJsdgjus99ZnYA2tYnPS80mebBEd4O4FNVEUd34v3B5FkgotxlS7qdcSg5MG7nwAgzG7MjzF_GX6mn/s1600-h/lingkaran3.JPG"><img style="cursor: pointer; width: 400px; height: 152px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvtQjUGNnr5i-ORTjOWDAgwPEn8h_9Ck7GeZIZpqR_kixeFNLDGR-LkL41Gtoe1SNJsdgjus99ZnYA2tYnPS80mebBEd4O4FNVEUd34v3B5FkgotxlS7qdcSg5MG7nwAgzG7MjzF_GX6mn/s400/lingkaran3.JPG" alt="" id="BLOGGER_PHOTO_ID_5370573924701149026" border="0" /></a><br /></div><br />=======================================================================<br /><br />Bagaimana penyelesaian yang tepat untuk soal yang sebelumnya?<br /><div style="text-align: justify;">Saya sendiri belum menemukan solusi yang tepat. Mungkin pembaca bisa membantu menemukan solusi yang tepat dan bersedia menshare jawaban Anda di kolom comment di bawah. :)..<br /></div><br /><div style="border-left: 3px dashed rgb(255, 0, 0); padding: 4px; background: rgb(255, 229, 159) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; color: rgb(0, 0, 0);">Sumber soal: buku "Kumpulan Soal Unik Matematika" oleh Tobi Moektijono.<br /></div></span>hendry_dexthttp://www.blogger.com/profile/00040950406506290844noreply@blogger.com9