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Old Seemingly Simple Putnam Problem

Source: 1959 Putnam

October 28, 2020
Putnam

Problem Statement

"Let ω3=1,ω≠1\omega^3 = 1, \omega \neq 1. Show thatz1,z2,−ωz1,−ω2z2z_1, z_2, -\omega z_1, -\omega^2z_2 are the vertices of an equilateral triangle."
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