Solution
= Solution
The <Euclidean division> gives $a=qb+r$ with $q\in\mathbb N_0$ and $0\le r<b$. Writing $a=nu,b=nv$ gives
$$
r=a-qb=n(u-qv).
$$
Since $u-qv$ is an <integer>, this proves the <divisibility>
$$
\boxed{n\mid r,}
$$
including $r=0$.