Definition:Divisor (Algebra)/Natural Numbers

Definition
Let $\N$ be the natural numbers.

Let $n \in \N$ and $m \in \N_{>0}$.

Then $m$ divides $n$ is defined as:
 * $m \mathrel \backslash n \iff \exists p \in \N: m \times p = n$

To indicate that $m$ does not divide $n$, we write $m \nmid n$.

Also known as
If $m \mathrel \backslash n$, then:
 * $m$ is a divisor (or factor) of $n$
 * $n$ is a multiple of $m$
 * $n$ is divisible by $m$.

The conventional notation for this is "$m \mid n$", but there is a growing trend to follow the notation above, as espoused by Knuth etc.