Number theory includes elementary number theory and advanced number theory.

Elementary number theory is a number theory studied by elementary methods. In essence, its research method is to use the divisibility of integer rings, including divisibility theory, congruence theory and continued fraction theory. Advanced number theory includes more profound mathematical research tools. It includes algebraic number theory, analytic number theory and computational number theory.

Development of number theory

Number theory was called arithmetic in the early days. It was not until the beginning of the 20th century that the name number theory was used. The word arithmetic means "basic operation". However, in the second half of the 20th century, some mathematicians still used the word "arithmetic" to represent number theory.

1952, mathematician Harold Davenport still used the word "advanced arithmetic" to represent number theory. When Godfrey Harold Hardy and Edward Maitland Wright wrote Introduction to Number Theory at 1938, they mentioned that "we considered changing the title to Introduction to Arithmetic, which is a more suitable title to some extent, but it is also convenient for readers to read.