ABSTRACT
This chapter focuses on the important role in computer science in general and in cryptography in particular. It turns out, however, that we can form finite sets from the integers which themselves have interesting algebraic structures. The key tool for forming these sets is an important idea defined on the integers which was originally developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. Probably without realizing it, students have already encountered congruences in everyday life.
