For which $n,m$ is $\Bbb Q(w)\subseteq \Bbb Q(\zeta)$, where $w$ and $\zeta$ are primitive $n$ and $m$th roots of unity respectively.
And, what are the cyclotomic extensions containing $i$?
the answer is :"if and only if n|m or n|2m with m odd"
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2 years ago