ABSTRACT
Congruences are a natural and convenient notation for formulating many interesting assertions in number theory. In this chapter, we introduce and work with congruences, we show how to solve linear congruences, and we use congruences to present three key theorems: Fermat’s theorem, Euler’s theorem, and Wilson’s theorem. We also discuss applications of congruences to parity check codes, e.g., the ones used in the ISBN (International Standard Book Number) system.
