IMO Shortlist 2018 problem A1


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3. listopada 2019.
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Let \mathbb{Q}_{>0} denote the set of all positive rational numbers. Determine all functions f:\mathbb{Q}_{>0}\to \mathbb{Q}_{>0} satisfying f(x^2f(y)^2)=f(x)^2f(y)for all x,y\in\mathbb{Q}_{>0}

Izvor: https://www.imo-official.org/problems/IMO2018SL.pdf