# Number Theory

Number theory (or arithmetic) is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well as the properties of objects made out of integers (e.g., rational numbers) or defined as generalizations of the integers (e.g., algebraic integers).

Integers can be considered either in themselves or as solutions to equations (diophantine geometry). Questions in number theory are often best understood through the study of analytical objects (e.g., the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, e.g., as approximated by the latter (diophantine approximation).

The older term for number theory is arithmetic. By the early twentieth century, it had been superseded by "number theory". (The word "arithmetic" is used by the general public to mean "elementary calculations"; it has also acquired other meanings in mathematical logic, as in Peano arithmetic, and computer science, as in floating point arithmetic.) The use of the term arithmetic for number theory regained some ground in the second half of the 20th century, arguably in part due to French influence. In particular, arithmetical is preferred as an adjective to number-theoretic.

### Other articles related to "number theory, theory, numbers, number":

Number Theory - Literature
... An introduction to the theory of numbers (rev ... Elements of Number Theory (reprint of the 1954 ed.) ... Number theory ...
List Of Triangle Topics - Number Theory - Integers in Geometry
... Heronian triangle Integer triangle Pythagorean triple Triangular number. ...
Ludwig Stickelberger - Mathematical Contributions - Number Theory
... Three joint papers with Frobenius deal with the theory of elliptic functions ... in his formulation of the reciprocity laws in algebraic number fields ... field as a module over its abelian Galois group (cf Iwasawa theory) ...
List Of People From Tamil Nadu - Scholars - Mathematics
... Pillai (1901–1950), known for his work in number theory Kollagunta Gopalaiyer Ramanathan (1920–1992), known for his achievements in number theory C ... Ramanujam (1938–1974), worked on number theory and algebraic geometry T ... (1902–1955), worked on Pisot-Vijayaraghavan number Ravindran Kannan, Professor of Computer Science and Mathematics at Yale University ...
Multiple Zeta Function - References
... series related to the Riemann zeta function", Journal of Number Theory 19 (1) 85–102, doi10.1016/0022-314X(84)90094-5, ISSN 0022-314X, MR 0751166 Crandall, Richard E ... other multiple zeta-functions", Proceedings of the Session in Analytic Number Theory and Diophantine Equations, Bonner Math ... Number Theory 6 (3) 501–514 ...

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