# The Relation of Congruence

Chapter

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## Abstract

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.

## References

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

## Copyright information

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