Generator of all congruence classes Is it possible for $\langle a \rangle =\mathbb Z/n\mathbb Z^*$ for $a\in  \mathbb Z/n\mathbb Z^*$?
I think I recall hearing it is, what is the name this element takes? I remember hearing generator but i'm not sure.

Such an $a$ is a generator of the multiplicative group modulo $n$, and is called a primitive root modulo $n$. They don't exist for all $n$, but they do always exist when $n$ is a prime number.
