Let $G$ be a finite group s.t. $|G|=p^rm$, where $(p,m)=1$.
Let then $P$ be a $p$-Sylow subgroup of $G$, i.e. $P\le G$ with $|P|=p^r$.
We want to show that $|G:N_G(P)|$ is the number of $p$-Sylow subgroups of $G$.
I made several attempts but nothing good came out.
Any help/answer/hint will be appreciated so much; thank you all.