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, 2023

Algebra Difficulty 5.0 AIME, harder Prove it Hungary

Let $f(x)=x^2-2$ . Let $f^{(n)}(x)$ denote the $n^{\text{th}}$ iterate of $f$ (i.e. $f^{(1)}(x)=f(x)$ and $f^{(k+1)}(x)=f\big(f^{(k)}(x)\big)$ ).

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