chapter  5
16 Pages

Induction and Fermat

Having learned the basic facts of modular arithmetic, we are now ready to return to the study of prime numbers. The main result of this chapter is a very useful theorem first proved by Fermat. This theorem is in fact a straightforward consequence of a much deeper theorem in group theory, which we will learn about in Chapter 8. In this chapter, however, we follow Fermat’s lead and give a direct proof of the theorem using finite induction. It is with a description of this method of proof that we begin.