modular arithmetic - congruency Suppose $a$ is an integer, and $a\equiv 4 \pmod{13}$. Find the $c$ with $0\leq c \leq12$, and $c \equiv9a\pmod{13}.$ I'm mildly confused by this problem because I don't understand what the value of $a$ is. Can the value of $a$ vary? I have a whole list of problems to do and I'm drawing a blank.

Yes, the value of $a$ can vary, but only such that the given condition on $a$ is fulfilled. So $a$ can be $4$, $17$, $30$, etc., and also $-9$, $-22$, and so on.

The important part, though, is that $a$ leaves a remainder of $4$ when divided by $13$. What then is the remainder of $9a$, when divided by $13$?