Arithmetic

Arithmetic or arithmetics (from the Greek word αριθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though in usage by professional mathematicians, it often is treated as a synonym for number theory. It is the oldest, most fundamental and simplest branch of mathematics, used widely by almost everyone from simple daily counting to more advanced science and business.

Number theory

The term arithmetic is also used to refer to number theory. This includes the properties of integers related to primality, divisibility, and the solution of equations by integers, as well as modern research which is an outgrowth of this study. It is in this context that one runs across the fundamental theorem of arithmetic and arithmetic functions. A Course in Arithmetic by Serre reflects this usage, as do such phrases as first order arithmetic or arithmetical algebraic geometry.

Related Topics:
Number theory - Primality - Divisibility - Solution of equations by integers - Fundamental theorem of arithmetic - Arithmetic function - Serre

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Number theory, while a well established discipline, has not reached a point where authorities agree on even basic principles which should apply.

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