ABSTRACT
D ivisibility is a key concept in number theory. The main purposeof this chapter is to introduce some basic concepts and properties that relate to divisibility. Some of them, such as divisibility, divisors, common divisors, the least common multiples, and factorization, have already been taught in middle school and high school. Here we shall define them by a precise mathematical language. Through mastering mathematical definitions and properties of these concepts, we can further solve many elementary number theoretic problems related to divisibility. The theory of divisibility has a rich content and provides flexible problem-solving methods. It not only is the foundation of number theory and algebra, but also has a wider range of applications to cryptography. Some important applications in cryptography include prime factorization of integers, and the Euclidean algorithm for finding greatest common divisors.
