ABSTRACT
This is an introductory chapter. The main topic is the arithmetic of congruences, sometimes called “clock arithmetic.” It leads to the construction of the integers modulo n. These are among the simplest examples of groups, as we shall see in Chapter 5. If n is a prime number, then the integers modulo n form a field. In Chapter 4, we will be looking at matrices with entries in these fields. As an application of congruences, we also discuss divisibility tests. In order to be able to solve linear congruences, we review greatest common divisors and the Euclidean algorithm.
