jasperE3 wrote: Find all polynomials $P(x)$ with real coefficieints such that $P\left(x^2\right)=P(x)P(x-1)$ for all $x\in\mathbb R$. See https://artofproblemsolving.com/community/c6h555999p3231281 (which considered only degrees nonzero, so you'll just have to add the two constant solutions)