MathDB
2048th Roots of Unity

Source:

August 8, 2024
algebracomplex numbers2022

Problem Statement

Let ω\omega be a complex number satisfying ω2048=1\omega^{2048} = 1 and ω1024≠1\omega^{1024} \neq 1. Find the unique ordered pair of nonnegative integers (p,q)(p, q) satisfying 2p−2q=∑0≤m<n≤2047(ωm+ωn)2048. 2^p - 2^q = \sum_{0 \leq m < n \leq 2047} (\omega^m + \omega^n)^{2048}.
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