## ABSTRACT

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.