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I am trying to prove the following statement,

Let ω be a complex nth root of unity. We say that ω is a primitive nth root if $\omega^m\neq1$ for any positive $m < n$. Prove that for all $n\in\mathbb{N}$, the sum of the primitive complex nth roots of unity is $\mu(n)$.

I know this somehow involves the Mobius inversion formula but aside from this I do not know how to progress. Any help would be greatly appreciated!

Anne Bauval
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Mathsbot69
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  • @AnneBauval I'm very new to Number Theory, thank you for your response but I am unfamiliar with this concept and do not seem to understand it even after reading it. Is it ok if you could explain the relation in simpler terms? – Mathsbot69 Dec 15 '22 at 16:31
  • Hi @Mathsbot69 I wrote a much simpler answer here. – Anne Bauval Dec 15 '22 at 18:29

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