IMO Shortlist 2016 problem A7


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3. listopada 2019.
2016 alg funkcija funkcijska shortlist
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Find all functions f:\mathbb{R}\rightarrow\mathbb{R} such that f(0)\neq 0 and for all x,y\in\mathbb{R}, f(x+y)^2 = 2f(x)f(y) + \max \left\{ f(x^2+y^2), f(x^2)+f(y^2) \right\}.

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