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Functional Eq

Author: daniyar
Problem has been solved: 15 times

Русский язык | English Language

Let $ f: Z \to Z $ be some function that takes positive values with positive values of the argument. It turned out that $f(x^2+y^2)+f(x^2-3y^2)=2f(x-y)(x+y)$ for any integers $ x $ and $ y $ and $ \sqrt{|f (2015) \cdot f(2016)|} $ is an integer. Find the smallest possible value of $ f (1) + f (2) $.

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