SILK-ROAD 2004 Problem 1

Find all $f: \mathbb{R} \to \mathbb{R}$ , such that $(x+y)(f(x)-f(y))=(x-y)f(x+y)$ for all real $x,y$ .

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.