## Abstract

This chapter is devoted to the elementary properties concerning the *relation of divisibility* in the set of integers, with a particular emphasis on the division algorithm, on the notion of greatest common divisor and the fundamental role played by prime numbers. In spite of the elementary character of the arguments we shall use, we will meet several interesting problems and results along the way, like Bézout’s theorem on the characterization of the greatest common divisor of two integers and Euclid’s theorem on the infinitude of primes.

## References

- 8.A. Caminha,
*An Excursion Through Elementary Mathematics I - Real Numbers and Functions*(Springer, New York, 2017)Google Scholar - 18.W. Fulton,
*Algebraic Curves*. Freely available at http://www.math.lsa.umich.edu/ wfulton - 20.C.R. Hadlock,
*Field Theory and its Classical Problems*(Washington, MAA, 2000)Google Scholar - 31.M. Reid,
*Undergraduate Algebraic Geometry*(Cambridge University Press, Cambridge, 1988)Google Scholar

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