Group actions in number theory
Abstract
Students having had a semester course in abstract algebra are exposed to the elegant way in which finite group theory leads to proofs of familiar facts in elementary number theory. In this note we offer two examples of such group theoretical proofs using the action of a group on a set. The first is Fermat's little theorem and the second concerns a well known identity involving the famous Euler phi function. The tools that we use to establish both results are sometimes seen in a second semester algebra course in which group actions are studied. Specifically, we will use the class equation of a group action and Burnside's theorem.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 August 2005
 DOI:
 10.48550/arXiv.math/0508396
 arXiv:
 arXiv:math/0508396
 Bibcode:
 2005math......8396H
 Keywords:

 History and Overview
 EPrint:
 5 pages