Along the same vein of another question I've posted is another question that merges group theory with number theory. I havn't taken a formal course on group theory, and is likely why I'm stumped at these questions posed from elementary number theory. The question goes as
Let $p$ be an odd prime and $g$ a generator of the group $(\mathbb{Z}/p \mathbb{Z})^*$. I need to show that either $g$ or $g+p$ is a generator of $(\mathbb{Z}/p^2 \mathbb{Z})^*$
I'm not sure where to begin. Just need a push in the right direction.
Thanks!