长春大学学报（自然科学版）2017，Vol.27Issue(2)：29-32,4.
有关费尔马小定理的推广
On Generalization of Fermats Little Theorem
摘要
Abstract
Firstly, Fermat's little theorem was proved by using mathematical induction.Secondly, the formula was obtained and Fermat's little theorem was proved by using algebraic structure of residues system multiplication of modulo p.Thirdly, this method was extended to the general residues system of modulo n and any finite abelian group.Finally, the same formula was established on finite non-abelian group by using Lagrange's theorem.The fact shows that Fermat's little theorem is a special case of the most basic Lagrange's theorem in group theory.关键词
交换群/非交换群/费尔马小定理/欧拉定理/拉格朗日定理Key words
abelian group/non-abelian group/Fermat's Little Theorem/Euler's Theorem/Lagrange's Theorem分类
数理科学引用本文复制引用
杨燕妮..有关费尔马小定理的推广[J].长春大学学报（自然科学版）,2017,27(2):29-32,4.基金项目
新疆维吾尔自治区自然科学基金项目(2016D01A014) （2016D01A014）
