A Geometric Proof of Fermat’s Little Theorem

¹ Florida Gulf Coast University, Fort Myers, USA

² Florida Gulf Coast University, Fort Myers, USA

³ Florida Gulf Coast University, Fort Myers, USA

Abstract

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-theo retic result. A lemma traditionally, if ambiguously, attributed to Burnside provides a critical enumeration step.

KeywordsFermatCarmichael NumberGroupPermutationBurnside’s LemmaActionInvariant SetOrbitStabilizerColoringPatternPrimeRegular PolygonCyclic Group

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A Geometric Proof of Fermat’s Little Theorem

Abstract

References (8)