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2012 BMO Problems/Problem 4

Revision as of 15:42, 1 January 2024 by Ddk001 (talk | contribs) (Created page with "==2012 BMO Problems/Problem 4 ==Problem== Find all functions <math>f : \mathbb{Z}^+ \to \mathbb{Z}^+</math> (where <math>\mathbb{Z}^+</math> is the set of positive integers) s...")
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==2012 BMO Problems/Problem 4

Problem

Find all functions $f : \mathbb{Z}^+ \to \mathbb{Z}^+$ (where $\mathbb{Z}^+$ is the set of positive integers) such that $f(n!) = f(n)!$ for all positive integers $n$ and such that $m - n$ divides $f(m) - f(n)$ for all distinct positive integers $m$, $n$.

Solution

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