When is $Aut\left(\mathbb{Z}_n\right)$ cyclic?
Where $Aut \left( G \right)$ is the group of "Automorphisms of the group $G$" under composition.
I know that $Aut\left(\mathbb{Z}_n\right) \approx U\left(n\right)$ but I don't know when $U\left(n\right)$ is cyclic.