# Unlucky Polynomial

Algebra Level 5

Suppose $$f(x)$$ is a polynomial of degree $$13$$ that satisfies the functional equation $f(2x^2-1)=2(f(x))^2-1$ Find the last three digits of the coefficient of $$x^5$$ in $$f$$.

Details and assumptions

The coefficient of $$x^5$$ is a positive integer.

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