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Polish MO Finals 2014, Problem 4

Source: Polish MO Finals 2014

July 27, 2016
contestsfunctionfunctional equation

Problem Statement

Denote the set of positive rational numbers by Q+\mathbb{Q}_{+}. Find all functions f:Q+→Q+f: \mathbb{Q}_{+}\rightarrow \mathbb{Q}_{+} that satisfy f(f(f(…f(f⏟n(q))… )))=f(nq)\underbrace{f(f(f(\dots f(f}_{n}(q))\dots )))=f(nq) for all integers n≥1n\ge 1 and rational numbers q>0q>0.
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