## Abstract

In this chapter, we return to the point of view of Example 2.21, looking at congruence modulo *n* as an *equivalence relation*. As a byproduct of our discussion, a number of interesting applications will be presented, among which is an alternative, simpler proof of Euler’s theorem. We will also introduce the quotient set \(\mathbb Z_n\) and show that it can be furnished with operations of *addition* and *multiplication* quite similar to those of \(\mathbb Z\). In particular, the case of \(\mathbb Z_p\), with *p* prime, will be crucial to our future discussion of polynomials.

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