IMO 2014 Shortlist A5
Consider all polynomials Ppxq with real coefficients that have the following property: for any two real numbers x and y ...
Category: Algebra
Problem
Consider all polynomials Ppxq with real coefficients that have the following property: for any two real numbers x and y one has |y2 ´ Ppxq| ď 2|x| if and only if |x2 ´ Ppyq| ď 2|y|. Determine all possible values of Pp0q. (Belgium)