## Description

Number theory is one of the oldest subjects in mathematics. Traditionally, number theory is the purest of the pure mathematical discipline. But with the advent of modern computers, it becomes more and more computation involved, giving to the birth of computational number theory, and even the quantum computational number theory, just as analytic number theory and algebraic number theory, where analysis and algebra play an important role. This chapter provides an introduction to the basic ideas and concepts, as well as some important open problems in number theory and computational number theory and quantum computational number theory. More speciﬁcally, we shall give a descriptive answer to the following three questions:

1. What is number theory?

2. What is computational number theory?

3. What is quantum computational number theory?