# 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 $f (1) + f (2)$.