# Recurrence and polynomials?

Algebra Level 5

Let $$f (x)=x^{3}+6$$.

Define a sequence of polynomials $$P_{n}(x)$$.

$$P_{1}(x)=f(x), P_{n+1}(x)=f (P_{n}(x)), n=1, 2, ...$$

Find the sum of all real solutions to the equation $$P_{2014}(x)=x$$. If the answer is $$S$$, find the greatest integer not exceeding $$10^{6}S$$.

This problem is part of the set ... and polynomials

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