AUSTRIAN-POLISH 1986 Problem 9

Find all continuous monotonic functions $f : R \to R$ that satisfy $f (1) = 1$ and $f(f (x)) = f (x)^2$ for all $x \in R$ .

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.