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What is the smallest positive integer \(n\) such that all the roots of \(z^4 - z^2 + 1 = 0\) are \(n^{\text{th}}\) roots of unity?

 

Thanks a lot! :)

 Jan 17, 2021
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Using exponential form, we can express the roots as e^(2*pi*i/18), e^(2*3*pi*i/18), e^(2*11*pi*i/18), and e^(2*17*pi*i/18).  Therefore, the smallest n that works is 18.

 Jan 17, 2021

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