# Poly polynomials

Level pending

Let $$P_1(x) = x^2 - 2$$ and $$P_i(x) = P_1 (P_{i-1}(x))$$ for $$i \geq 2$$. Let $$N$$ denote the number of real roots of $$P_{2014}(x)$$. Find the first three digits of $$\log_2{N}$$.

Details and assumptions

Each root is counted once, regardless of it's multiplicity.

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