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2025 IMO Problems/Problem 3

Let $\mathbb{N}$ denote the set of positive integers. A function $f: \mathbb{N} \rightarrow \mathbb{N}$ is said to be bonza if $f(a)$ divides $b^{a} - f(b)^{f(a)}$ for all positive integers $a$ and $b$. Determine the smallest real constant $c$ such that $f(n) \leq cn$ for all bonza functions $f$ and all positive integers $n$.

Video solution

https://www.youtube.com/watch?v=vPqUTG4CW8w

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