# what is the set of $\{ k : N\mid kc \}$ given $N$ and $c$?

Given $N, c$ such that $1 < c < N$. What is the following set?

$$S=\{ k : 1 \leq k \leq N \text{ and } N \mid kc \}$$

For example, if $\gcd(c,N)=1,$ then we know $S=\{N\}$. what about more general case?
Have you tried any examples? If $\text{gcd}(c,N)=d$, then $N/d$ is in the set. What else? –  Jonas Meyer Dec 7 '12 at 3:18
what about multiple of $d$? –  redplum Dec 7 '12 at 3:21
Don't think in terms of multiples of $d$, more like factors. –  André Nicolas Dec 7 '12 at 3:26