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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 Størmer number ： ウィキペディア英語版 Størmer number In mathematics, a Størmer number or arc-cotangent irreducible number, named after Carl Størmer, is a positive integer ''n'' for which the greatest prime factor of (''n''2 + 1) meets or exceeds 2''n''. The first few Størmer numbers are: : 1, 2, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 19, 20, ... . J. Todd proved that this sequence is neither finite nor cofinite. The Størmer numbers arise in connection with the problem of representing the Gregory numbers (arctangents of rational numbers) $G\_=\backslash arctan\backslash frac$ as sums of Gregory numbers for integers (arctangents of unit fractions). The Gregory number $G\_$ may be decomposed by repeatedly multiplying the Gaussian integer $a+bi$ by numbers of the form $n\backslash pm\; i$, in order to cancel prime factors ''p'' from the imaginary part; here $n$ is chosen to be a Størmer number such that $n^2+1$ is divisible by $p$.〔Conway & Guy (1996): 245, ¶ 3〕 ==Notes== 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「Størmer number」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.