\begin{definition}[Definition:Quotient (Algebra)]
Let $a, b \in \Z$ be integers such that $b \ne 0$.
From the Division Theorem:
:$\forall a, b \in \Z, b \ne 0: \exists_1 q, r \in \Z: a = q b + r, 0 \le r < \size b$
The value $q$ is defined as the '''quotient of $a$ on division by $b$''', or the '''quotient of $\dfrac a b$'''.
\end{definition}