There are at least 2016 fixed points of the function

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Anindya Biswas
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There are at least 2016 fixed points of the function

Unread post by Anindya Biswas » Mon May 10, 2021 9:41 am

Let $S=\{0,1,2,3,\cdots,10^{2017}+2005\}$. Let $f:S\to S$ be a function that satisfies \[f^{2017}(x)=\underbrace{f\circ f\circ f\circ\cdots\circ f(x)}_{2017}=x\]
Prove that there exists $T\subseteq S$ of $2016$ elements such that $\forall x\in T, f(x)=x$.
"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
John von Neumann

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