MathDB

Sum of complex numbers can be small

Source: HMIC 2021 Problem 3

May 4, 2021

HMICalgebra

Problem Statement

Let

A

be a set of

n\ge2

positive integers, and let

\textstyle f(x)=\sum_{a\in A}x^a

. Prove that there exists a complex number

z

with

\lvert z\rvert=1

and

\lvert f(z)\rvert=\sqrt{n-2}