A Geometric Proof of Fermat’s Little Theorem

• 作者: Andrew Orsini Marc Barry Thomas Beatty
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: Fermat Carmichael Number GROUP PERMUTATION Burnside’s LEMMA Action Invariant Set Orbit STABILIZER COLORING Pattern Prime Regular POLYGON Cyclic GROUP
• 年，卷（期）: 2018,（1）
• 页码范围: 41-44
• 页数: 4页
• 分类号: O1

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.