AUSTRIAN-POLISH 1978 Problem 1

Determine all functions $f:(0;\infty)\to \mathbb{R}$ that satisfy $f(x+y)=f(x^2+y^2) \forall x,y\in (0;\infty)$

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.