Find an automorphism "Let a and b be two generators of a finite cyclic group G. Show that there exists an automorphism of G that maps a to b"
Im thinking that I need to find a $\phi: G \rightarrow G$, if its possible to show that this $\phi$ is an isomorphism, then I have showed that there exists an automorphism. But how should I think to find such a $\phi$?
Maybe I should note that I know that G is abelian.

Hint: If $G$ is cyclic and generated by $x$ (and we write the group law as addition) then every element of $G$ can be written in the form $nx$ for some $n \in \mathbb Z$.
Similarly if $y$ is some other generator then every element of the group can be written in the form $ny$ for some $n \in \mathbb Z$.
