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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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new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

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new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia