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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 Sidon set ： ウィキペディア英語版 Sidon sequence In number theory, a Sidon sequence (or Sidon set), named after the Hungarian mathematician Simon Sidon, is a sequence ''A'' =  of natural numbers in which all pairwise sums ''a''''i'' + ''a''''j'' (''i'' ≤ ''j'') are different. Sidon introduced the concept in his investigations of Fourier series. The main problem in the study of Sidon sequences, posed by Sidon,〔. (Addendum ), 19 (1944), 208.〕 is to find the largest number of elements a Sidon sequence ''A'' can have smaller than some given number ''x''. Despite a large body of research,〔.〕 the question remained unsolved for almost 80 years. In 2010, it was finally settled by J. Cilleruelo, I. Ruzsa and C. Vinuesa. ==Early results== Paul Erdős and Pál Turán proved that, for every ''x'' > 0, the number of elements smaller than ''x'' in a Sidon sequence is at most $\backslash sqrt+O(\backslash sqrt())$. Using a construction of J. Singer, they showed that there exist Sidon sequences that contain $\backslash sqrt(1-o(1))$ terms less than ''x''. 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「Sidon sequence」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.