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For a nonnegative integer n define \text{rad}(n)=1 if n=0 or n=1, and \text{rad}(n)=p_1p_2\cdots p_k where p_1<p_2<\cdots <p_k are all prime factors of n. Find all polynomials f(x) with nonnegative integer coefficients such that \text{rad}(f(n)) divides \text{rad}(f(n^{\text{rad}(n)})) for every nonnegative integer n.

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