MathDB
P6: Complex numbers: 6|n and (alpha)^n=1

Source:

March 31, 2013

Problem Statement

Let α\alpha be a complex number such that both α\alpha and α+1\alpha+1 have modulus 11. If for a positive integer nn, 1+α1+\alpha is an nn-th root of unity, then show that α\alpha is also an nn-th root of unity and nn is a multiple of 66.
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