ZA-SAMO 2013 Problem 4

Determine all pairs of polynomials $f$ and $g$ with real coefficients such that $x^2 \cdot g(x) = f(g(x)).$

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.