IMO Shortlist 2016 problem A4


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Dodao/la: arhiva
3. listopada 2019.
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Find all functions f:(0,\infty)\rightarrow (0,\infty) such that for any x,y\in (0,\infty), xf(x^2)f(f(y)) + f(yf(x)) = f(xy) \left(f(f(x^2)) + f(f(y^2))\right).

Izvor: https://www.imo-official.org/problems/IMO2016SL.pdf