Definition 1. Let $n$, $m \in \N$. $n$ divides $m$, written
\[n \divides m,\]if there exists $k \in \N$ such that
\[m = kn.\]Note. ”$n$ divides $m$” is also phrased as:
- $n$ is a divisor or factor of $m$;
- $m$ is a multiple of $n$;
- $m$ is divisible by $n$.
-
For all $n \in \N$,
\[0 \divides n.\] -
For all $n \in \N^+$,
\[n \ndivides 0.\]