Fermat’s Theorem, II

Abstract

Fermat’s theorem says that if p is a prime number and a is any integer relatively prime to p, then a^p−1 ≡1 (modp). In Chapter I-11 we gave a proof based on the fact that the set of invertible elements of ℤ _p forms an abelian group of order p ™1. In this chapter we give another proof based on the binomial theorem. We begin by making a definition which relates to the fact that in ℤ _p , [p] = 0.