Prove that we always have $ 2n \mid \varphi(m^n+p^n) $

Question

For each $ a ∈ \Bbb N^*$, denoted by $\varphi (a) $ is the number of positive integers not exceeding $a$ and coprime to $a$.

Let $n, m, p ∈ \Bbb N^*, m \ne p$. Prove that we always have $2n \mid \varphi(m^n+p^n)$