# Tagged Questions

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### Fixed points of $x\mapsto 2^{2^{2^{2^x}}} \mod p$

Let $p$ be a prime. For how many elements $x$ of $\{0,1,\dotsc,p-1\}$ can it be the case that
$$2^{2^{2^{2^x}}} = x \mod p?$$
In particular, can you find a simple proof (or, even better, several ...