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A cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to $\mathbb Q$, the field of rational numbers.

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Can a sum of roots of unity be an integer?

If $n$ is square-free this cannot happen (even just for the case $k=n$), and if $n$ is not square-free (and in the case $k=n$) one must have the sum being zero if it is an integer (as seen in Peter Mu …
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