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$f$ is continuous on $[0,n]$ and $f(0) = f(n)$. Prove that there are $n$ different $(x,y)$(regardless of order) such that $f(x) = f(y)$ and $x - y \in \mathbb{Z}/\{0\}$.

I have no idea how to do it.

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  • $\begingroup$ Can I ask the source of this problem? If you can provide a reputable source, I would be happy to put a bounty on this to encourage solutions. $\endgroup$ May 13, 2019 at 21:22

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