MathDB

polynomial with complex coefficients

Source: IMC 2000 day 2 problem 3

October 29, 2005

algebrapolynomialcomplex numberscomplex analysis

Problem Statement

Let

p(z)

be a polynomial of degree

n>0

with complex coefficients. Prove that there are at least

n+1

complex numbers

z

for which

p(z)\in \{0,1\}