Disprove: There exist unique integers $q$ and $r$ such that $204=25q+r$.

Question

Disprove:

There exist unique integers $q$ and $r$ such that $204=25q+r$.

I need to use the division algorithm somehow, but I don't see how I can disprove it when it seems to be true.

Any help is appreciated, thanks!

Edit: It must follow that $0\le{r}<25$.

Answer 1

Consider $q=8，r=4$, and $q=9, r=-21$

Answer 2

There are no restrictions on $q$ and $r$. We first find one such pair by the division algorithm: $$204=25\cdot8+4\qquad q,r=8,4$$ Now add one to the quotient, and subtract 25 from the remainder to compensate, completing the disproof: $$204=25\cdot9-21\qquad q,r=9,-21$$