Let $\displaystyle \mathbb{Z}_{p^r} = \{ 0,1, \ldots, p^r -1\}$ be the ring of integers modulo $\displaystyle p^r$, a power of a prime. I was wondering if someone could help explain why there are $\displaystyle p^{r-1}$ elements that are coprime to $\displaystyle p^r $ in this ring? I am getting tangled up in knots and would appreciate any help with this.

Thanks very much.