Question 5
Let $a,b,c$ be integers satisfying $0\lt a\lt c-1$ and $1\lt b\lt c$. For $0\le k\le a$, let $r_k$, $0\le r_k\lt c$, be the remainder of $kb$ divided by $c$. Prove that the sets $\{r_0,r_1,\ldots,r_a\}$ and $\{0,1,\ldots,a\}$ are different.