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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?2012-12-07
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    what about multiple of $d$?2012-12-07
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    redplum, I don't understand your comment.2012-12-07
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    Don't think in terms of multiples of $d$, more like factors.2012-12-07
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    sorry, I meant multiple of N/d2012-12-07
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    redplum: Sounds like a good idea. Can you finish it?2012-12-07
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    got it, so S should contain all k2012-12-07

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