Division with remainder/Z/Fact

Then, for every integer number ${\displaystyle {}n}$, there exists a uniquely determined integer number ${\displaystyle {}q}$ and a uniquely determined natural number

${\displaystyle {}r}$, ${\displaystyle {}0\leq r\leq d-1}$, such that

${\displaystyle {}n=qd+r\,}$

holds.