威尔逊定理的一些推广的简单证明

IF 0.1 Q4 MATHEMATICS Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica Pub Date : 2014-12-01 DOI:10.2478/AUPCSM-2014-0001

J. Gorowski, Adam Łomnicki

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引用次数: 3

摘要

摘要本文给出了威尔逊定理的高斯推广的一个显著的简单证明。该证明是基于有限阿贝尔群的2阶元生成的子群的性质。给出了在n > 2为整数时等价于(Φ(n)，·n)的循环性的几个条件，特别是在该群中存在2阶唯一元素的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Simple proofs of some generalizations of the Wilson’s theorem

Abstract In this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group.

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来源期刊

Annales Universitatis Paedagogicae Cracoviensis-Studia Mathematica MATHEMATICS-

自引率

11.10%

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审稿时长

15 weeks