# More polynomials!

Algebra Level 5

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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