CL-MO 2021 Problem 3

Find all polynomials $p(x)$ with real coefficients that satisfy $4p(x^2) = 4(p(x))^2 + 4p(x)- 1$

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.