Question 71
Find all non-negative real numbers $c \ge 0$ such that there exists a function $f : (0, +\infty) \to (0, +\infty)$ with the property
$$
f(y^2 f(x) + y + c) = x f(x + y^2)
$$
for all $x, y \gt 0$.
$$
f(y^2 f(x) + y + c) = x f(x + y^2)
$$
for all $x, y \gt 0$.