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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 Kaplansky's theorem on quadratic forms ： ウィキペディア英語版 Kaplansky's theorem on quadratic forms In mathematics, Kaplansky's theorem on quadratic forms is a result on simultaneous representation of primes by quadratic forms. It was proved in 2003 by Irving Kaplansky.〔.〕 ==Statement of the theorem== Kaplansky's theorem states that a prime ''p'' congruent to 1 modulo 16 is representable by both or none of ''x''2 + 32''y''2 and ''x''2 + 64''y''2, whereas a prime ''p'' congruent to 9 modulo 16 is representable by exactly one of these quadratic forms. This is remarkable since the primes represented by each of these forms individually are ''not'' describable by congruence conditions.〔.〕 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「Kaplansky's theorem on quadratic forms」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.