TUYMAADA 1999 Problem 2

Find all polynomials $P(x)$ such that $P(x^3+1)=P(x^3)+P(x^2).$

Proposed by A. Golovanov

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.