PAMO 2003 Problem 6

Find all functions $f: R\to R$ such that: $f(x^2)-f(y^2)=(x+y)(f(x)-f(y)), x,y \in R$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.