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Old 14 ¡Ñ¹ÂÒ¹ 2013, 15:37
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Old 24 Á¡ÃÒ¤Á 2016, 10:40
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ú¡Ç¹ ⨷Âìã¹áºº½Ö¡ËÑ´¹Õé˹è͹ФР¢Íº¤Ø³¤èÐ

8. ¨§ËҨӹǹàµçÁ $x$ áÅÐ $y$ ·Ø¡¤Ùè·Õèà»ç¹¤ÓµÍº¢Í§ÊÁ¡Òà $x^4+(x+1)^4=y^2+(y+1)^2$

10. ¨§áÊ´§ÇèÒÊÁ¡Òà $x^2+y^2=z^3$ Áդӵͺà»ç¹¨Ó¹Ç¹àµçÁºÇ¡ä´éäÁè¨Ó¡Ñ´¨Ó¹Ç¹

11. ¡Ó˹´ÊÁ¡Òà $x^2+y^2=z^2+18$ àÁ×èÍ $x,y$ áÅÐ $z$ à»ç¹¨Ó¹Ç¹àµçÁºÇ¡
(11.1) ¨§¾ÔÊÙ¨¹ìÇèÒ $z$ ¨Ðµéͧà»ç¹¨Ó¹Ç¹¤Ùè
(11.2) ¨§¾ÔÊÙ¨¹ìÇèÒ ÊÁ¡ÒùÕéÁդӵͺÍÂÙèã¹ÃÙ» $z=y+1$ äÁè¨Ó¡Ñ´ªØ´
(11.3) ¨§¾ÔÊÙ¨¹ìÇèÒ ÊÁ¡ÒùÕéäÁèÁդӵͺã¹ÃÙ» $z=y+5$
(11.4) ¨§¾ÔÊÙ¨¹ìÇèÒ ÊÁ¡ÒùÕéäÁèÁդӵͺ $x,y,z$ ·ÕèàÃÕ§¡Ñ¹à»ç¹ÅӴѺàÅ¢¤³Ôµ
(11.5) ¨§¾ÔÊÙ¨¹ìÇèÒ ÊÁ¡ÒùÕéäÁèÁդӵͺ $x,y,z$ ·ÕèàÃÕ§¡Ñ¹à»ç¹ÅӴѺàâҤ³Ôµ
(11.6) ¨§ËҤӵͺ¢Í§ÊÁ¡ÒùÕéÁÒÊÑ¡ 1 ªØ´ àÁ×èÍ $x=y$
(11.7) ¨§¾ÔÊÙ¨¹ìÇèÒ ÊÁ¡ÒùÕéÁդӵͺäÁè¨Ó¡Ñ´ªØ´àÁ×èÍ $x=y$

12. ¨§áÊ´§ÇèÒ ·Ø¡æ¨Ó¹Ç¹àµçÁºÇ¡ $z$ ¨ÐÁըӹǹàµçÁ $x$ áÅÐ $y$ ·ÕèÊÍ´¤Åéͧ¡ÑºÊÁ¡Òà $x^2-y^2=z^3$

13. ¨§áÊ´§ÇèÒ ÊÁ¡ÒÃä´âÍΌ䷹ì $5m^2-6mn+7n^2=1988$ äÁèÁդӵͺ

15. ãËé $n$ à»ç¹¨Ó¹Ç¹àµçÁ ¨§¾ÔÊÙ¨¹ìÇèÒ ¶éÒ $2+2\sqrt{28n^2+1} $ à»ç¹¨Ó¹Ç¹àµçÁ áÅéǨӹǹ´Ñ§¡ÅèÒǹÕé¨Ðà»ç¹¡ÓÅѧÊͧÊÁºÙóì
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Old 25 Á¡ÃÒ¤Á 2016, 13:26
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ÍéÒ§ÍÔ§:
10. ¨§áÊ´§ÇèÒÊÁ¡Òà $x^2+y^2=z^3$ Áդӵͺà»ç¹¨Ó¹Ç¹àµçÁºÇ¡ä´éäÁè¨Ó¡Ñ´¨Ó¹Ç¹
ÊÃéÒ§¤ÓµÍºªØ´§èÒÂÁÒ $1$ ªØ´ àÃÕ¡ÇèÒ $(x_0,y_0,z_0)$ ¨Ò¡¹Ñé¹ãËé

$x=x_0t^3,y=y_0t^3,z=z_0t^2$ àÁ×èÍ $t\in\mathbb{N}$
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  #4  
Old 31 ¸Ñ¹ÇÒ¤Á 2016, 19:32
MathBlood's MathBlood's äÁèÍÂÙèã¹Ãкº
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13.äªémod3
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