KöMaL problem A, 2025

Number theory Difficulty 5.0 AIME, harder Prove it Hungary

Let $a \geq 3$ be an integer, and define $f(n) = a^n - 1$ for every positive integer $n$ . Denote by $f^{(k)}$ the $k$ -iterate of $f$ , that is, $f^{(1)}(n) = f(n)$ and $f^{(k+1)}(n)=f(f^{(k)}(n))$ for $k \geq 1$ .

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