CZ-SK-MO 1993 Problem 5

Find all functions $f : Z \to Z$ such that $f(-1) = f(1)$ and $f(x)+ f(y) = f(x+2xy)+ f(y-2xy)$ for all $x,y \in Z$

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.