Show that $n\bmod m$ is periodic $\forall n,m \in \mathbb{N}^+$

Question

How can I show that $n\bmod m$ is periodic?

If I have a simple example like $n\bmod6 \equiv a$ how can I show that this is periodic if e.g $f(n) = n\bmod6$?

Answer 1

Hint: A function $f$ is periodic with period $m$ if $f(n+m)=f(n)$ for all $n$.