Issue with Root of Unity Proof

Asked Jan 20 '19 at 20:05

Active Jan 20 '19 at 20:05

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I need some help with a proof:

Let $gcd(k,n)=1, w_n = e^{2*\pi*i/n}$ and $w_n^k = e^{2*\pi*i*k/n}$. Show that the equation $ <w_n> = <w_n^k>$ holds, where $<x>$ = {$x^n|n \in N_0 $}

Is it necessary to show, that $w_n^k$ is primitive, if $gcd(k,n)=1$ holds?

asked Jan 20 '19 at 20:05

Mow

Yes, it is necessary. But it has been shown already here, i.e., $g^k$ is also a generator, if and only if $gcd(n,k)=1$. – Dietrich Burde Jan 20 '19 at 20:09
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Issue with Root of Unity Proof

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