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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 Frobenius pseudoprime ： ウィキペディア英語版 Frobenius pseudoprime In number theory, a Frobenius pseudoprime is a pseudoprime that passes a specific probable prime test described by Jon Grantham in a 1998 preprint and published in 2000. It has been studied by other authors for the case of quadratic polynomials. ==Frobenius pseudoprimes w.r.t. quadratic polynomials== Frobenius pseudoprimes are defined with respect to a fixed monic polynomial. The case of a degree-2 (quadratic) polynomial $\backslash scriptstyle\; x^2\; -\; Px\; +\; Q$, where $\backslash scriptstyle\; D\; =\; P^2-4Q$ is not a square, is common and can be expressed in terms of Lucas sequences $U\_n(P,Q)$ and $V\_n(P,Q)$, leading to fast implementations for testing pseudoprimality. A composite number ''n'' is a Frobenius $(P,Q)$ pseudoprime if and only if $\backslash textstyle\backslash gcd(n,2QD)=1$, :$(1)\; \backslash qquad\; U\_(P,Q)\; \backslash equiv\; 0\; \backslash pmod\; n$ and : where $\backslash scriptstyle\; k=\backslash left(\backslash tfrac\backslash right)$ is the Jacobi symbol. Both conditions hold for all primes, hence this constitutes a probable prime test. Condition (1) is the same condition that defines a Lucas pseudoprime, hence every Frobenius $(P,Q)$ pseudoprime is also a Lucas $(P,Q)$ pseudoprime, but because of the additional condition (2), the converse is not true. 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「Frobenius 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.