Editing Divisor (section)

== Definition ==
An [[integer]] <math>n</math> is divisible by a nonzero integer <math>m</math> if there exists an integer <math>k</math> such that <math>n=km.</math> This is written as
: <math>m\mid n.</math>
This may be read as that <math>m</math> divides <math>n,</math> <math>m</math> is a divisor of <math>n,</math> <math>m</math> is a factor of <math>n,</math> or <math>n</math> is a multiple of <math>m.</math> If <math>m</math> does not divide <math>n,</math> then the notation is <math>m\not\mid n.</math>{{sfn|ps=|Hardy|Wright|1960|p=1}}{{sfn|ps=|Niven|Zuckerman|Montgomery|1991|p=4}}

There are two conventions, distinguished by whether <math>m</math> is permitted to be zero:
* With the convention without an additional constraint on <math>m,</math> <math>m \mid 0</math> for every integer <math>m.</math>{{sfn|ps=|Hardy|Wright|1960|p=1}}{{sfn|ps=|Niven|Zuckerman|Montgomery|1991|p=4}}
* With the convention that <math>m</math> be nonzero, <math>m \mid 0</math> for every nonzero integer <math>m.</math>{{sfn|ps=|Sims|1984|p=42}}{{sfnp|ps=|Durbin|2009|p=57|loc=Chapter III Section 10}}