BALKAN 2007 Problem 2

Find all real functions $f$ defined on $\mathbb R$ , such that $f(f(x)+y) = f(f(x)-y)+4f(x)y ,$ for all real numbers $x,y$ .

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.