OBM 2010 Problem 1

Find all functions $f$ from the reals into the reals such that $f(ab) = f(a+b)$ for all irrational $a, b$ .

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.