Question 3
Find all functions $f:\mathbb Z\to\mathbb Z$ satisfying
$$xf(2f(y)-x)+y^2f(2x-f(y))=\frac{f(x)^2}{x}+f(yf(y))$$
for every pair of integers $x,y$ with $x\ne0$.
Proposed by Titu Andreescu (as credited in the supplied compilation).
$$xf(2f(y)-x)+y^2f(2x-f(y))=\frac{f(x)^2}{x}+f(yf(y))$$
for every pair of integers $x,y$ with $x\ne0$.
Proposed by Titu Andreescu (as credited in the supplied compilation).