for which integers $\displaystyle c$ with $\displaystyle 0 \leq c < 1001$ does the congruence $\displaystyle 154x \equiv c$ $\displaystyle (\bmod 1001)$ have solutions? For each case when there are solutions, find how many solutions are not congruent modulo 1001.

Originally, I thought this problem might have something to do with multiplicative inverses, but I didn't get anywhere on that front.

If it matters, I calculated $\displaystyle \gcd (154,1001)$ to be 77.