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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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    got it, so S should contain all kN/d| k. – 2019-03-14

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