Congruence Classes

  • Antonio Caminha Muniz Neto
Part of the Problem Books in Mathematics book series (PBM)


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.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Antonio Caminha Muniz Neto
    • 1
  1. 1.Universidade Federal do CearáFortalezaBrazil

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