Competition problem — Number theory

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Number theory Difficulty 6.3 National olympiad Prove it

Example
2
Given that $f(x)$ is a polynomial with integer coefficients, $p$ is a prime number, and $k$ is a positive integer.
Prove: $(f(x))^{p^{p^{k}}} \equiv f\left(x^{p^{p^{2}}}\right)(\bmod p)$ .

Solution

None

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