Number theory is a branch of pure mathematics, which mainly studies the properties of integers. Integer can be the solution of the equation (Diophantine equation). Some analytic functions (such as Riemannian functions) include some properties of integers and prime numbers.

Through these functions, we can also understand some problems of number theory. The relationship between real numbers and rational numbers can also be established by number theory, and real numbers can be approximated by rational numbers (Diophantine approximation).