In a question, it was asked to prove that if $p$ is an odd prime, $n>0$ and $0
${p^n\choose k}\equiv 0 \pmod {p^n}$
My question is, is the hypothesis $p$ is an odd prime necessary? I have worked out a proof, but without using the fact that $p$ is odd, ie., my proof seems to work perfectly for $p=2$.
Sincere thanks for help.