Let $a,b \in \mathbb{N}$, let $\mathbb{N}_0:=\{0\}\cup\mathbb{N}$, and regard $\mathbb{N}_0$ as a subset of $\mathbb{Z}$ with its usual addition, multiplication, and order. Then there exist unique $q,r \in \mathbb{N}_0$ such that $a=qb+r$ in $\mathbb{Z}$ and $0 \le r < b$.