# Prime Polynomial Pickle

For every prime $$p$$ consider all polynomials $$f(x)$$ with integer coefficients from $$1$$ to $$p$$ and degree at most $$p-1$$, such that for all integers $$x$$ the number $$f(2x)-f(x)$$ is divisible by $$p$$.

Find the sum of all primes $$p<1000$$ such that the number of such polynomials is strictly greater than $$p\cdot2^{p-2}$$.

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