IrMO 2010 Problem 5

Find all polynomials $f(x)=x^3+bx^2+cx+d$ , where $b,c,d,$ are real numbers, such that $f(x^2-2)=-f(-x)f(x)$ .

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.