The Theorems of Fermat, Wilson and Euler

Abstract

These three theorems, especially the one by Euler, play a central role in many modern applications, such as digital encryption. They are deeply related to the theory of groups, and indeed, their most elegant proofs are group theoretic. Here, however, we shall stress the purely arithmetic viewpoint. We also introduce the important Euler Ф function (or totient function) which reaches into every corner of number theory and which, by way of illustration, tells us how many ways an n-pointed star can be drawn by n straight lines without lifting the pen.