There are at least 2016 fixed points of the function
Posted: 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 $\forall x\in T, f(x)=x$.
Prove that there exists $T\subseteq S$ of $2016$ elements such that $\forall x\in T, f(x)=x$.