Theorem $3\mathrm{.}7.[$The division algorithm.$]$ If each of a and $b$ is an integer with qra$=bq+r\mathrm{.}0rso$ that:

$a=bq+r\mathrm{.}0$ then there exist unique integers $q$ and $r$ with $0rso$ that:

$a=bq+r.$