MathDB

Miklós Schweitzer 2004, Problem 8

Source: Miklós Schweitzer 2004

July 30, 2016

college contestsMiklos Schweitzercomplex numberscomplex analysisreal analysis

Problem Statement

Prove that for any

0<\delta <2\pi

there exists a number

m>1

such that for any positive integer

n

and unimodular complex numbers

z_1,\ldots, z_n

with

z_1^v+\dots+z_n^v=0

for all integer exponents

1\le v\le m

, any arc of length

\delta

of the unit circle contains at least one of the numbers

z_1,\ldots, z_n