$m^4 - 1 \vert m^{4^{n+1}} - 1$ ???

there was a typo, instead of $m^{4^{ n+1}} - 1$ the correct is $m^{4^ n+1} - 1$

This is twice the same ideas imbricated.

parmenides51 wrote: Let $m$ and $n$ be positive integers. Prove that if $m^{4^n+1} - 1$ is a prime number, then there exists an integer $t \ge 0$ such that $n = 2^t$. But for every $n$ $m^{4^n+1} - 1$ is divisible by $m-1$ so $m$ must be $2$ to make $m^{4^n+1} - 1$ a prime number ??