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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 Diophantine quintuple ： ウィキペディア英語版 Diophantine quintuple In mathematics, a diophantine ''m''-tuple is a set of ''m'' positive integers $\backslash$ such that $a\_i\; a\_j\; +\; 1$ is a perfect square for any .〔 Diophantus himself found the set $\backslash left\backslash ,\; \backslash frac4,\; \backslash frac\backslash right\backslash \}$ of rationals which has the property that each $a\_i\; a\_j\; +\; 1$ is a rational square.〔 More recently, sets of six positive rationals have been found. The first diophantine quadruple was found by Fermat: $\backslash$.〔 It was proved in 1969 by Baker and Davenport 〔 that a fifth positive integer cannot be added to this set. However, Euler was able to extend this set by adding the rational number $\backslash frac$.〔 No (integer) diophantine quintuples are known, and it is an open problem whether any exist.〔 Dujella has shown that at most a finite number of diophantine quintuples exist. ==References== 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「Diophantine quintuple」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.