%0 Journal Article
%T A Geometric Proof of Fermat¡¯s Little Theorem
%A Thomas Beatty
%A Marc Barry
%A Andrew Orsini
%J Advances in Pure Mathematics
%P 41-44
%@ 2160-0384
%D 2018
%I Scientific Research Publishing
%R 10.4236/apm.2018.81004
%X We present an intuitively satisfying geometric proof
of Fermat's result for positive integers that ![\"\"](\"Edit_0b50006d-6c00-4238-bfe4-e54f91b8720a.bmp\")
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.
%K Fermat
%K Carmichael Number
%K Group
%K Permutation
%K Burnside¡¯s Lemma
%K Action
%K Invariant Set
%K Orbit
%K Stabilizer
%K Coloring
%K Pattern
%K Prime
%K Regular Polygon
%K Cyclic Group
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=81916