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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 Legendre's equation ： ウィキペディア英語版 Legendre's equation In mathematics, Legendre's equation is the Diophantine equation :$ax^2+by^2+cz^2=0.$ The equation is named for Adrien Marie Legendre who proved in 1785 that it is solvable in integers ''x'', ''y'', ''z'', not all zero, if and only if −''bc'', −''ca'' and −''ab'' are quadratic residues modulo ''a'', ''b'' and ''c'', respectively, where ''a'', ''b'', ''c'' are nonzero, square-free, pairwise relatively prime integers, not all positive or all negative . ==References== * L. E. Dickson, ''History of the Theory of Numbers. Vol.II: Diophantine Analysis'', Chelsea Publishing, 1971, ISBN 0-8284-0086-5. Chap.XIII, p. 422. * J.E. Cremona and D. Rusin, "Efficient solution of rational conics", Math. Comp., 72 (2003) pp. 1417-1441. () 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「Legendre's equation」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.