# Order Of A Polynomial Shuffle

For how many possible values of $n$, can one find a polynomial with integer coefficients $f(x)$ and pair-wise distinct integers $x_1,x_2,...,x_n,$ such that $0\leq x_i \leq 24$ for all $i$ and $\begin{cases}f(x_1)\equiv x_2 \pmod {25}\\ f(x_2)\equiv x_3 \pmod {25}\\ \ ...\\ f(x_n)\equiv x_1 \pmod {25} \ ?\end{cases}$

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