Question 73
Let $f: \mathbb{Z} \rightarrow \mathbb{Z}$ be a function such that for any integers $x, y$, we have
$$
f\left(x^{2}-3 y^{2}\right)+f\left(x^{2}+y^{2}\right)=2(x+y) f(x-y)
$$
Suppose that $f(n)\gt 0$ for all $n\gt 0$ and that $f(2015) \cdot f(2016)$ is a perfect square. Find the minimum possible value of $f(1)+f(2)$.
$$
f\left(x^{2}-3 y^{2}\right)+f\left(x^{2}+y^{2}\right)=2(x+y) f(x-y)
$$
Suppose that $f(n)\gt 0$ for all $n\gt 0$ and that $f(2015) \cdot f(2016)$ is a perfect square. Find the minimum possible value of $f(1)+f(2)$.