Composition is real implies polynomials are real
Source: India Postal Set 5 P 3 2016
January 18, 2017
algebrapolynomial
Problem Statement
Call a non-constant polynomial real if all its coecients are real. Let and be polynomials with complex coefficients such that the composition P \circ Q is real. Show that if the leading coefficient of and its constant term are both real, then and are real.