Let $x$ be a residue$\mod p$ where $p$ is an odd prime.
Im searching for such $p$ such that there exists a function $f(x)$ with propery
$f(f(x)) - 2^x \equiv 0 \mod p $
for all values of $x$.
I got this question from here :
http://math.eretrandre.org/tetrationforum/showthread.php?tid=940