In this chapter, we introduce the basic notions of divisibility, primes, and unique factorization. The division algorithm and the Euclidean algorithm are the fundamental tools necessary for the study of divisibility properties of integers. The chapter includes a discussion of prime numbers, a proof of the Fundamental Theorem of Arithmetic, and properties of the greatest common divisor.
An application of the Euclidean algorithm is to the solution of linear Diophantine problems. The projects at the end the chapter explore Pythagorean triples, perfect numbers, and Goldbach's conjecture. In addition, there is an extensive discussion on prime numbers, and elementary factorization methods such as factorization by trial division and Fermat's factoring method.