# 2020 CAMO Problems/Problem 5

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## Problem 5

Let $f(x)=x^2-2$. Prove that for all positive integers $n$, the polynomial $$P(x)=\underbrace{f(f(\ldots f}_{n\text{ times}}(x)\ldots))-x$$can be factored into two polynomials with integer coefficients and equal degree.