I am looking for a reference or proof for the following problem:

Problem: Let $r$ be prime, then $2r$ is a Sylow $p$-number if and only if $2r=1+p^{2n}$. 2r=1+p^{2^n}$. Thanks in advance.

I am looking for a reference or proof for the following problem:

Problem: Let $r$ be prime, then $2r$ is a Sylow $p$-number if and only if $2r=1+p^{2n}$. Thanks in advance.