Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study.
Number theory may be subdivided into several fields, according to the methods used and the type of questions investigated. (See the list of number theory topics.)
The terms "arithmetic" or "the higher arithmetic" as nouns are also used to refer to elementary number theory. These are somewhat older terms, which are no longer as popular as they once were. However the word "arithmetic" is popularly used as an adjective rather than the more cumbersome phrase "number-theoretic", and also "arithmetic of" rather than "number theory of"; e.g., arithmetic geometry, arithmetic functions, arithmetic of elliptic curves.
In elementary number theory, integers are studied without use of techniques from other mathematical fields. Questions of divisibility, use of the Euclidean algorithm to compute greatest common divisors, integer factorizations into prime numbers, investigation of perfect numbers and congruences belong here.
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