# Unique Monic Polynomials

Algebra 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.

×