AUSTRIAN-POLISH 1984 Problem 9

Find all functions $f: Q \to R$ satisfying $f (x + y) = f (x)f (y) - f(xy) + 1$ for all $x,y \in Q$

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.