AUSTRIAN-POLISH 2003 Problem 1

Find all real polynomials $p(x)$ such that $p(x-1)p(x+1)= p(x^2-1)$ .

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.