MathDB

5

Part of 2017 IMC

Problems(1)

IMC 2017 Problem 5

Source:

8/2/2017
Let kk and nn be positive integers with n≥k2−3k+4n\geq k^2-3k+4, and let f(z)=zn−1+cn−2zn−2+⋯+c0f(z)=z^{n-1}+c_{n-2}z^{n-2}+\dots+c_0 be a polynomial with complex coefficients such that c0cn−2=c1cn−3=⋯=cn−2c0=0c_0c_{n-2}=c_1c_{n-3}=\dots=c_{n-2}c_0=0 Prove that f(z)f(z) and zn−1z^n-1 have at most n−kn-k common roots.
imc 2017IMCpolynomialcomplex analysis