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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fermat's right triangle theorem ： ウィキペディア英語版 Fermat's right triangle theorem Fermat's right triangle theorem is a non-existence proof in number theory, the only complete proof left by Pierre de Fermat. It has several equivalent formulations: *If three square numbers form an arithmetic progression, then the gap between consecutive numbers in the progression (called a congruum) cannot itself be square. *There do not exist two Pythagorean triangles in which the two legs of one triangle are the leg and hypotenuse of the other triangle. *A right triangle for which all three side lengths are rational numbers cannot have an area that is the square of a rational number. An area defined in this way is called a congruent number, so no congruent number can be square. *A right triangle and a square with equal areas cannot have all sides commensurate with each other. *The only rational points on the elliptic curve $y^2=x(x-1)(x+1)$ are the three trivial points (0,0), (1,0), and (−1,0). *The Diophantine equation $x^4-y^4=z^2$ has no integer solution. An immediate consequence of the last of these formulations is that Fermat's last theorem is true for the exponent $n=4$. == Formulation == 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fermat's right triangle theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.