A pair (f, g) of degree 2 real polynomials is called foolish if f(g(x))=f(x) \cdot g(x) for all real x. How many positive integers less than 2023 can be a root of g(x) for some foolish pair (f, g)?
A pair (f, g) of degree 2 real polynomials is called foolish if f(g(x))=f(x) \cdot g(x) for all real x. How many positive integers less than 2023 can be a root of g(x) for some foolish pair (f, g)?