divisibility

Given integers $a$ and $b$, then we say $a$ divides $b$ if and only if there is some $q\in \mathbb{Z}$ such that $b=qa$.

There are many other ways in common use to express this relationship:

• $a\mid b$ (read “$a$ divides $b$”).

• $b$ is divisible by $a$.

• $a$ is a factor of $b$.

• $a$ is a divisor of $b$.

• $b$ is a multiple of $a$.

The notion of divisibility can apply to other rings (e.g., polynomials).

Title	divisibility
Canonical name	Divisibility
Date of creation	2013-03-22 11:59:49
Last modified on	2013-03-22 11:59:49
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	11
Author	mathcam (2727)
Entry type	Definition
Classification	msc 11A51
Synonym	divides
Synonym	divisor
Synonym	factor
Synonym	multiple
Related topic	LeastCommonMultiple
Related topic	ExampleOfGcd
Related topic	TauFunction
Related topic	ExactlyDivides
Related topic	DivisorSumOfAnArithmeticFunction
Related topic	StrictDivisibility
Related topic	FundamentalTheoremOfArithmetic
Related topic	NumberTheory