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Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions [1] the book reviews over three millennia of research on numbers but the key focus is on mathematicians from the 17th century to the 19th, in particular, on the works of the mathematicians fermat, euler, lagrange, and legendre paved the. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers).

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations An approach through history from hammurapi to legendre is a book on the history of number theory, written by andré weil and published in 1984 Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique

[3] multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and dirichlet's theorem on primes in arithmetic.

List of number theory topics this is a list of topics in number theory List of recreational number theory topics topics in cryptography It is named for g Littlewood, who developed it in a series of papers on waring's problem.

Glossary of number theory this is a glossary of concepts and results in number theory, a field of mathematics Concepts and results in arithmetic geometry and diophantine geometry can be found in glossary of arithmetic and diophantine geometry See also list of number theory topics. Geometry of numbers, also known as geometric number theory, is the part of number theory which uses geometry for the study of algebraic numbers

Typically, a ring of algebraic integers is viewed as a lattice in and the study of these lattices provides fundamental information on algebraic numbers

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