# 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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