Division Algorithm

Type: definition

Given positive integers $b$ and $a$ with $b>a$, there exists a unique pair $(q,r)$ satisfying
\[
  b=qa+r
\]
with
\[
  0\le r<a.
\]

We refer to each variable as follows:
\[
\begin{aligned}
  b&:\ \text{dividend},\\
  a&:\ \text{divisor},\\
  q&:\ \text{quotient},\\
  r&:\ \text{remainder}.
\end{aligned}
\]