Definition:Remainder

Let $$a, b \in \Z$$.

From the Division Theorem, we have that:


 * $$\forall a, b \in \Z, b \ne 0: \exists! q, r \in \Z: a = q b + r, 0 \le r < \left|{b}\right|$$

The value $$r$$ is defined as the principal remainder of $$a$$ on division by $$b$$, or the principal remainder of $$\frac {a}{b}$$.