Unique Monic PolynomialsAlgebra Level 5
How many monic polynomials with real coefficients of degree \(<1000\) have the property that \(f(x^2+x)=(f(x))^2+f(x)\) for all \(x\)?
Details and assumptions
A polynomial is monic if its leading coefficient is 1. For example, the polynomial \( x^3 + 3x - 5 \) is monic but the polynomial \( -x^4 + 2x^3 - 6 \) is not.