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IMC 2017 Problem 5

Source:

August 2, 2017
imc 2017IMCpolynomialcomplex analysis

Problem Statement

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.
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