IMOR 2017 - Problem 2
Source: 1st International Mathematical Olympic Revenge
July 22, 2017
IMORalgebra
Problem Statement
A polynomial is good if it has integer coefficients, it is monic, all its roots are distinct, and there exists a disk with radius on the complex plane that contains all the roots. Prove that there is no good polynomial for a sufficient large degree.Proposed by Rodrigo Sanches Angelo (rsa365), Brazil.