1. ## Generator

Let $p$ be a prime number. Then how many generators of the cyclic group $Z_{p^r}$, with $r\in\mathbb{Z}$ and $r\ge 1$

2. Originally Posted by GTK X Hunter
Let $p$ be a prime number. Then how many generators of the cyclic group $Z_{p^r}$, with $r\in\mathbb{Z}$ and $r\ge 1$

$\mbox{An element}\,\,x\in Z_{p^r}\,\,\mbox{is a generator iff}\,\,(x,p^r)=1\,\,\mbox{, so there are....generators}$

Tonio

3. Originally Posted by tonio
$\mbox{An element}\,\,x\in Z_{p^r}\,\,\mbox{is a generator iff}\,\,(x,p^r)=1\,\,\mbox{, so there are....generators}$

Tonio
you mean the gcd $(x,p^r)=1$?