# 2007 UNCO Math Contest II Problems/Problem 4

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## Problem

If $x$ is a primitive cube root of one (this means that $x^3 =1$ but $x \ne 1$) compute the value of $$x^{2006}+\frac{1}{x^{2006}}+x^{2007}+\frac{1}{x^{2007}}.$$