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

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

What can we say about this set?

For example, if $\gcd(c,N)=1,$ then we know $S=\{N\}$. what about more general case?

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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
    
redplum, I don't understand your comment. – Jonas Meyer Dec 7 '12 at 3:26
    
Don't think in terms of multiples of $d$, more like factors. – André Nicolas Dec 7 '12 at 3:26
    
sorry, I meant multiple of N/d – redplum Dec 7 '12 at 6:45

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