SOLUTION: What is the smallest positive integer {{{n}}} such that all the roots of {{{z^4 + z^2 + 1 = 0}}} are the nth root of unity?

SOLUTION: What is the smallest positive integer {{{n}}} such that all the roots of {{{z^4 + z^2 + 1 = 0}}} are the nth root of unity?

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Question 1065775: What is the smallest positive integer such that all the roots of are the nth root of unity?
Answer by ikleyn(52847) (Show Source): You can put this solution on YOUR website!
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What is the smallest positive integer such that all the roots of are the nth root of unity?
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All the roots of this polynomial ARE the 6-th roots of unity.

The number "n" you are asking for is 6.

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