Topological generator of the additive group of p-adic integers
= Topological generator of the additive group of p-adic integers
An element $\alpha\in\mathbb Z_p$ topologically generates the additive group of $\mathbb Z_p$ exactly when $\alpha\not\equiv0\pmod p$, equivalently when $\alpha$ is a <p-adic unit>. In that case its image generates every cyclic quotient $\mathbb Z/p^n\mathbb Z$.