Let p:C→C be a polynomial with degree n and complex coefficients which satisfies x∈R⟺p(x)∈R. Show that n=1
Problem
Source: Replacement IMO 1980 in Mersch - P2 - BE2
Tags: algebra, polynomial, algebra proposed
Source: Replacement IMO 1980 in Mersch - P2 - BE2
Tags: algebra, polynomial, algebra proposed
Let p:C→C be a polynomial with degree n and complex coefficients which satisfies x∈R⟺p(x)∈R. Show that n=1