If $n, m \in N^*$ and a group homomorphism $f: Z_n \to Z_m$. Show that $f(Z_n) =0$ if and only if $(n, m)=1$.
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What have you done so far for this question? – Soby May 16 '17 at 03:00
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We known that $Z_n. Z_m$ is cyclic if and only if $(n,m)=1$. But I don't use this to solve the problem. – Vũ Nguyễn Đình May 16 '17 at 03:11