IMO Shortlist 2010 problem A5


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June 23, 2013
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Denote by \mathbb{Q}^+ the set of all positive rational numbers. Determine all functions f : \mathbb{Q}^+ \mapsto \mathbb{Q}^+ which satisfy the following equation for all x, y \in \mathbb{Q}^+: f\left( f(x)^2y \right) = x^3 f(xy).

Proposed by Thomas Huber, Switzerland
Source: Međunarodna matematička olimpijada, shortlist 2010