# Another Functional Equation

Algebra Level 5

$f(xy)=f \left ( \frac{x^2+y^2}{2} \right ) + (x-y)^2$

Let $$f:\mathbb{R} \to \mathbb{R}$$ be a function satisfing the above statement. If $$f(0)=1$$, find the sum of all values of $$f(2017)$$.

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