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Complex numbers: a^2+a+1/a+1/a^2+1=0

Source: ISI(BS) 2007 #1

April 10, 2012

trigonometrymodular arithmeticalgebra proposedalgebra

Problem Statement

Suppose

a

is a complex number such that

a^2+a+\frac{1}{a}+\frac{1}{a^2}+1=0

m

is a positive integer, find the value of

a^{2m}+a^m+\frac{1}{a^m}+\frac{1}{a^{2m}}