A Geometric Proof of Fermat’s Little Theorem

作     者：Thomas Beatty Marc Barry Andrew Orsini 

作者机构：Florida Gulf Coast University Fort Myers USA 

出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)

年 卷 期：2018年第8卷第1期

页      面：41-44页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Fermat Carmichael Number Group Permutation Burnside’s Lemma Action Invariant Set Orbit Stabilizer Coloring Pattern Prime Regular Polygon Cyclic Group 

摘      要：We present an intuitively satisfying geometric proof of Fermat s result for positive integers that for prime moduli p, provided p does not divide a. This is known as Fermat’s Little Theorem. The proof is novel in using the idea of colorings applied to regular polygons to establish a number-theoretic result. A lemma traditionally, if ambiguously, attributed to Burnside provides a critical enumeration step.