IMO functional equations

Algebra Level 4

\(\mathbb R^+\) denotes the set of all positive real numbers. There exists only one function \(f : \mathbb {R^+ \to R^+}\) which satisfies

\[\large\ \\ xf\left(x^2\right) f\left( f(y)\right) + f\left( yf(x) \right) = f(xy) \left( f\left( f\left(x^2 \right) \right) + f\left( f\left(y^2\right)\right)\right) \]

for all positive real numbers \(x\) and \(y\).

Then find the numerical value of \(\large\ f\left( \frac { 1 }{ 2017 } \right)\).


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