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Homedivision algorithm for integers

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# 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 $0\leq r<b$. $q$ 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).

Related:

ExistenceAndUniquenessOfTheGcdOfTwoIntegers

Synonym:

division algorithm

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

11A51*no label found*

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## Recent Activity

Jul 5

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias