ABSTRACT
In Chapter 14, we studied the Gaussian integers and saw how they can be used to answer questions about the usual integers. In the present chapter, we consider the more general situation of quadratic fields and algebraic integers. These also have interesting applications, and we include a few. But we also encounter a situation where there is no unique factorization into irreducibles and show how this causes difficulties. The material in this chapter is the beginning of the subject called algebraic number theory, which started in the 1800s and is still an active area of research.
