The Relation of Congruence

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


In this chapter, we define and explore the most basic properties of the important relation of congruence modulo n > 1. Our central goal is to prove the famous Fermat’s little theorem, as well as its generalization, due to Euler. The pervasiveness of these two results in elementary Number Theory owes a great deal to the fact that they form the starting point for a systematic study of the behavior of the remainders of powers of a natural number a upon division by a given natural number n > 1, relatively prime with a. We also present the no less famous Chinese remainder theorem, along with some interesting applications.


  1. 8.
    A. Caminha, An Excursion Through Elementary Mathematics I - Real Numbers and Functions (Springer, New York, 2017)Google Scholar

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© 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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