Division with remainder/Z/Fact

Division with remainder (${}\mathbb {Z}$)

Let ${}d$ be a fixed positive natural number.

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

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

${}n=qd+r\,$

holds.

Write a proof