Integers, Divisors, and Primes

Abstract

In this chapter we discuss properties of integers. This area of mathematics is called number theory, and it is a truly venerable field: Its roots go back about 2500 years, to the very beginning of Greek mathematics. One might think that after 2500 years of research, one would know essentially everything about the subject. But we shall see that this is not the case: There are very simple, natural questions that we cannot answer; and there are other simple, natural questions to which an answer has been found only in the last few years!