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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