TITLE:
A Geometric Proof of Fermat’s Little Theorem
AUTHORS:
Thomas Beatty, Marc Barry, Andrew Orsini
KEYWORDS:
Fermat, Carmichael Number, Group, Permutation, Burnside’s Lemma, Action, Invariant Set, Orbit, Stabilizer, Coloring, Pattern, Prime, Regular Polygon, Cyclic Group
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.1,
January
24,
2018
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.