I need to find all the values of $a$ and $n$ that gives $\{0,a\}$ is a subgroup of the group $(\mathbb{Z}_n,+)$. Assum $n \geq 2$ and $a \neq 0$.
Actually I thing that for each $a$ and $n$ we will get that this is a subgroup ($0$ identity element) Am I wrong??