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#1
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![]() (2^8)+(2^10)+(2^n)=m^2 àÁ×èÍ m,n à»ç¹¨Ó¹Ç¹àµçÁºÇ¡ ¨§ËÒ¤èÒ n ·Õèà»ç¹ä»ä´é·Ñé§ËÁ´
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#2
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![]() ¶éÒ $n\leq 10$ ¨Ðä´é $n=4,10$
ÊÁÁµÔ $n>10$ ¨Ðä´é $2^8(2^{n-8}+5)=m^2$ ¨Ðä´éÇèÒ $2^{n-8}+5$ µéͧà»ç¹¡ÓÅѧÊͧÊÁºÙÃ³ì «Öè§à»ç¹ä»äÁèä´éã¹ modulo $8$
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site:mathcenter.net ¤Ó¤é¹ |
#3
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![]() ÍÕ¡ÇԸչФÃѺ
$5\times 2^8=(m-2^{\frac{n}{2}})(m+2^{\frac{n}{2}})$ ËÅѧ¨Ò¡¹Ñé¹´ÙµÑÇ»ÃСͺ¢Í§¨Ó¹Ç¹·Ò§«éÒ·Ñé§ËÁ´9¤Ùè ÁÕ2¤Ùè·Õè à¢éÒà§×è͹ä¢â¨·Âì¤×Í $(16,80) áÅÐ (32,40)$ ¨Ðä´éÇèÒÁÕ¤èÒ n ·Õèà¢éÒà§×è͹ä¢â¨·Âì ¤×Í 4 áÅÐ 10 ¤ÃѺ |
#4
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![]() ¤Ø³Nooonuii ¤Ø³Artty60 ¢Íº¤Ø³¤ÃѺ
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#5
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ÇÔ¸Õ¹Õéµéͧàªç¤¡è͹ÁÑé¤ÃѺÇèÒ $n$ µéͧà»ç¹àÅ¢¤Ùè
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#6
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![]() â´ÂÊèǹµÑǼÁ¤Ô´ÇèÒµÑÇ»ÃСͺ¢Í§¨Ó¹Ç¹··Ò§«éÒÂÁÕ18µÑÇËÃ×Í9¤Ùè ¹Ñé¹¹Óä»ãªé¶×Íà»ç¹¡ÒÃàªç¤ä»ã¹µÑÇ(ä´éÃÖà»ÅèÒ?)
äÁè·ÃÒºÇèÒ·èÒ¹nooonuiiÇèÒÍÂèÒ§äêèÇÂá¹Ð¹Ó˹èͤÃѺ 24 ¡Ã¡®Ò¤Á 2014 07:13 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 1 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ artty60 |
#7
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![]() ÍéÒ§ÍÔ§:
«Öè§àÃÒãªé¡ÒÃᡵÑÇ»ÃСͺẺ¨Ó¹Ç¹àµçÁäÁèä´é¹èÐÊÔ¤ÃѺ ¨ÐÁաóÕÍÂèÒ§àªè¹ á¡à»ç¹ $(5\sqrt{2})(128\sqrt{2})=(m-2^{n/2})(m+2^{n/2})$ Ẻ¹ÕéÂѧÁÕÍÕ¡àÂÍÐàÅ·Õè¨Ðµéͧàªç¤ ¡àÇé¹ÇèÒ¨Ðãªéà¤Ã×èͧÁ×Í˹ѡÍÂèÒ§¾Ç¡ algebraic number theory áµè¢é͹ÕéäÁèµéͧä»ä¡Å¢¹Ò´¹Ñé¹ËÃÍ¡
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#8
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![]() àËç¹´éǤÃѺ ¢Íº¤Ø³ÁÒ¡¤ÃѺ
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