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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