Let $G=\langle a\rangle$ be a cyclic group. Let $\eta\in\mathrm{End}\langle a\rangle$. Then "$\eta\in\mathrm{Aut}\langle a\rangle\Leftrightarrow \eta(a)$ is a generator of $\langle a\rangle$". Proof. If $\left |\langle a\rangle\right |=\in…