Originally Posted by

**georgel** Let $\displaystyle p$ be odd prime number such that $\displaystyle 2p+1$ is prime as well. Let$\displaystyle n=4p+2. $ Identify $\displaystyle Aut(\mathbb{Z}_n).$

Here's what I did.

$\displaystyle Aut(\mathbb{Z}_n)$ is isomorphic to the group $\displaystyle U_{\phi(n)}=($numbers relatively prime to $\displaystyle n, ._n)$, where $\displaystyle \phi(n)$ denotes the number of these numbers relatively prime to $\displaystyle n$.

But what is this group..?

Also, $\displaystyle \mathbb{Z}_n=\mathbb{Z}_{2(2p+1)}$ which is isomophic to $\displaystyle \mathbb{Z}_2 \oplus \mathbb{Z}_{2p+1}$, but that doesn't get me anywhere either.

Please help, thank you.