Proof:The quotient and remainder are unique
From CS2800 wiki
Assume that want to show that and .and and that both and are between 0 and . We
We havePlugging this back in to the equation , so . This means that is a multiple of ; it could be any of . However, since we have and , we have . Thus, the only possible value of is 0, so . shows that either or . Since we have defined the quotient and remainder by , we must have , so and thus .