Question 54
Find all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ such that
$$
x f(2 f(y)-x)+y^{2} f(2 x-f(y))=\frac{(f(x))^{2}}{x}+f(y f(y)),
$$
for all $x, y \in \mathbb{Z}, x \neq 0$.
$$
x f(2 f(y)-x)+y^{2} f(2 x-f(y))=\frac{(f(x))^{2}}{x}+f(y f(y)),
$$
for all $x, y \in \mathbb{Z}, x \neq 0$.