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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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Products of cyclotomic polynomials

Try $x^{30}+x^{20}+x^{15}+x^{10}+1=\Phi_6\Phi_{30}\Phi_{25}$. For more general solutions see the extended comment below. One way to search for such examples is to solve for the set of polynomials …
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