翻訳と辞書 Words near each other ・ Ramanujan (disambiguation) ・ Ramanujan (film) ・ Ramanujan graph ・ Ramanujan Institute for Advanced Study in Mathematics ・ Ramanujan IT City ・ Ramanujan Mathematical Society ・ Ramanujan prime ・ Ramanujan Prize ・ Ramanujan summation ・ Ramanujan tau function ・ Ramanujan theta function ・ Ramanujan's congruences ・ Ramanujan's lost notebook ・ Ramanujan's master theorem ・ Ramanujan's sum ・ Ramanujan's ternary quadratic form ・ Ramanujan–Nagell equation ・ Ramanujan–Petersson conjecture ・ Ramanujan–Sato series ・ Ramanujan–Soldner constant ・ Ramanujapur ・ Ramanujapuram, Thanjavur ・ Ramanujar (TV series) ・ Ramanujganj ・ Ramapala ・ Ramapati Ram Tripathi ・ Ramaperta ・ Ramaperta perarmata ・ Ramaperta telemaca ・ Ramapo Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Ramanujan's ternary quadratic form ： ウィキペディア英語版 Ramanujan's ternary quadratic form In mathematics, in number theory, Ramanujan's ternary quadratic form is the algebraic expression ''x''2 + ''y''2 + 10''z''2 with integral values for ''x'', ''y'' and ''z''. Srinivasa Ramanujan considered this expression in a footnote in a paper published in 1916 and briefly discussed the representability of integers in this form. After giving necessary and sufficient conditions that an integer cannot be represented in the form ''ax''2 + ''by''2 + ''cz''2 for certain specific values of ''a'', ''b'' and ''c'', Ramanujan observed in a footnote: "(These) results may tempt us to suppose that there are similar simple results for the form ''ax''2 + ''by''2 + ''cz''2 whatever are the values of ''a'', ''b'' and ''c''. It appears, however, that in most cases there are no such simple results."〔 To substantiate this observation, Ramanujan discussed the form which is now referred to as Ramanujan's ternary quadratic form. ==Properties discovered by Ramanujan== In his 1916 paper〔 Ramanujan made the following observations about the form ''x''2 + ''y''2 + 10''z''2. *The even numbers which are not of the form ''x''2 + ''y''2 + 10''z''2 are 4λ(16μ + 6). *The odd numbers that are not of the form ''x''2 + ''y''2 + 10''z''2, viz. 3, 7, 21, 31, 33, 43, 67, 79, 87, 133, 217, 219, 223, 253, 307, 391, . . . do not seem to obey any simple law. 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「Ramanujan's ternary quadratic form」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.