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Interesting functions

Author: mathforces
Problem has been solved: 12 times

Русский язык | English Language

We call a function $f: \mathbf{N} \xrightarrow{} \mathbf{N}$ interesting if $f^{f^{f(n)}(n)}(n)=n$ for every positive integer $n$. Find the sum of all positive integers $a$ such that $f^{2020} (a) = a$ for every interesting function $f$.
Remark: $f^k (n)$ means $\underbrace{f(f(...f(n)))}_{k \text{ times}}$

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