翻訳と辞書 Words near each other ・ Euler diagram ・ Euler equations (fluid dynamics) ・ Euler filter ・ Euler force ・ Euler function ・ Euler Granda ・ Euler Hermes ・ Euler Hydro-triplane ・ Euler integral ・ Euler line ・ Euler method ・ Euler number ・ Euler number (physics) ・ Euler operator ・ Euler product ・ Euler pseudoprime ・ Euler Renato Westphal ・ Euler sequence ・ Euler Society ・ Euler spiral ・ Euler substitution ・ Euler summation ・ Euler system ・ Euler tour technique ・ Euler's conjecture ・ Euler's continued fraction formula ・ Euler's criterion ・ Euler's critical load ・ Euler's Day Off ・ Euler's Disk 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 Euler pseudoprime ： ウィキペディア英語版 Euler pseudoprime In arithmetic, an odd composite integer ''n'' is called an Euler pseudoprime to base ''a'', if ''a'' and ''n'' are coprime, and : $a^\; \backslash equiv\; \backslash pm\; 1\backslash pmod$ (where ''mod'' refers to the modulo operation). The motivation for this definition is the fact that all prime numbers ''p'' satisfy the above equation which can be deduced from Fermat's little theorem. Fermat's theorem asserts that if ''p'' is prime, and coprime to ''a'', then ''a''''p''−1 = 1 (mod ''p''). Suppose that ''p''>2 is prime, then ''p'' can be expressed as 2''q'' + 1 where ''q'' is an integer. Thus; ''a''(2''q''+1) − 1 = 1 (mod ''p'') which means that ''a''2''q'' − 1 = 0 (mod ''p''). This can be factored as (''a''''q'' − 1)(''a''''q'' + 1) = 0 (mod ''p'') which is equivalent to ''a''(''p''−1)/2 = ±1 (mod ''p''). The equation can be tested rather quickly, which can be used for probabilistic primality testing. These tests are twice as strong as tests based on Fermat's little theorem. Every Euler pseudoprime is also a Fermat pseudoprime. It is not possible to produce a definite test of primality based on whether a number is an Euler pseudoprime because there exist ''absolute Euler pseudoprimes'', numbers which are Euler pseudoprimes to every base relatively prime to themselves. The absolute Euler pseudoprimes are a subset of the absolute Fermat pseudoprimes, or Carmichael numbers, and the smallest absolute Euler pseudoprime is 1729 = 7×13×19. ==Relation to Euler-Jacobi pseudoprimes== The slightly stronger condition that : $a^\; \backslash equiv\; \backslash left(\backslash frac\backslash right)\; \backslash pmod\; n$ where ''n'' is an odd composite, the greatest common divisor of ''a'' and ''n'' equals 1, and (''a''/''n'') is the Jacobi symbol, is the more common definition of an Euler pseudoprime. See, for example, page 115 of the book by Koblitz listed below, page 90 of the book by Riesel, or page 1003 of. A discussion of numbers of this form can be found at Euler–Jacobi pseudoprime. There are no absolute Euler-Jacobi pseudoprimes. Euler pseudoprimes to base 2 are :341, 561, 1105, 1729, 1905, 2047, 2465, 3277, 4033, 4681, 5461, 6601, 8321, 8481, 10261, 10585, 12801, 15709, 15841, 16705, 18705, ... 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「Euler pseudoprime」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.