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.
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