More polynomials!

Algebra Level 4

Let \(f(x)\) be a polynomial with \(f(1)=1\). It has the property that for some integer \(k \in [1,2015]\),

\[f(f(x))=f(x)^{ k }\]

Define \(p(x)\) as the sum of all possible polynomials that satisfy these conditions. Find the value of the following sum: \[\sum _{p(x )=0} x^{2016}\]

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