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-theoretic result. A lemma traditionally, if ambiguously, attributed to Burnside provides a critical enumeration step.
Highlights
A Geometric Proof of Fermat’s Little TheoremHow to cite this paper: Beatty, T., Barry, M. and Orsini, A. (2018) A Geometric Proof of Fermat’s Little Theorem
We present an intuitively satisfying geometric proof of Fermat’s result for positive integers that a p−1 ≡ 1 for prime moduli p, provided p does not divide a
We present a proof of this useful theorem from an intuitively appealing direction based on coloring the vertices of regular polygons with prime numbers of sides
Summary
How to cite this paper: Beatty, T., Barry, M. and Orsini, A. (2018) A Geometric Proof of Fermat’s Little Theorem. How to cite this paper: Beatty, T., Barry, M. and Orsini, A. (2018) A Geometric Proof of Fermat’s Little Theorem. Received: December 27, 2017 Accepted: January 21, 2018 Published: January 24, 2018
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