division algorithm for integers

Given any two integers $a,b$ where $b>0$, there exists a unique pair of integers $q,r$ such that $a=qb+r$ and . $q$ is called the quotient of $a$ and $b$, and $r$ is the remainder.

The division algorithm is not an algorithm at all but rather a theorem. Its name probably derives from the fact that it was first proved by showing that an algorithm to calculate the quotient of two integers yields this result.

There are similar forms of the division algorithm that apply to other rings (for example, polynomials).

Title	division algorithm for integers
Canonical name	DivisionAlgorithmForIntegers
Date of creation	2013-03-22 11:59:43
Last modified on	2013-03-22 11:59:43
Owner	vampyr (22)
Last modified by	vampyr (22)
Numerical id	7
Author	vampyr (22)
Entry type	Theorem
Classification	msc 11A51
Synonym	division algorithm
Related topic	ExistenceAndUniquenessOfTheGcdOfTwoIntegers