Question 45
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that
$$
\left(x^{2}+y^{2}\right) f(x y)=f(x) f(y) f\left(x^{2}+y^{2}\right)
$$
for all real $x$ and $y$.
$$
\left(x^{2}+y^{2}\right) f(x y)=f(x) f(y) f\left(x^{2}+y^{2}\right)
$$
for all real $x$ and $y$.