Question 22
Find all bijections $f: (0, +\infty) \to (0, +\infty)$ such that, for any $x, y \gt 0$ the following is satisfied:
$$
f(xf(x) + yf(y)) = f^2(x) + f^2(y).
$$
(Oleksii Masalitin, Fedir Yudin)
$$
f(xf(x) + yf(y)) = f^2(x) + f^2(y).
$$
(Oleksii Masalitin, Fedir Yudin)