Question 49
Let $a,b,c$ be integers satisfying $0<a<c-1$ and $1<b<c$. For each integer $k$ with $0\le k\le a$, let $r_k$ be the remainder when $kb$ is divided by $c$, so that $0\le r_k<c$.
Prove that
$$
\{r_0,r_1,\ldots,r_a\}\ne\{0,1,\ldots,a\}.
$$
Prove that
$$
\{r_0,r_1,\ldots,r_a\}\ne\{0,1,\ldots,a\}.
$$