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#1
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[˹ѧÊ×Í ÊÍǹ.] ÊÁ¡ÒÃä´âÍΌ䷹ì
¨Ò¡Ë¹Ñ§Ê×Í ÊÍǹ.¹Ð¤ÃѺ
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#2
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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 |
#3
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ÍéÒ§ÍÔ§:
$x=x_0t^3,y=y_0t^3,z=z_0t^2$ àÁ×èÍ $t\in\mathbb{N}$
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site:mathcenter.net ¤Ó¤é¹ |
#4
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13.äªémod3
15.ÅͧäËé¡é͹ã¹ÃÙ·=k^2 |
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