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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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Is there a pattern for the irreducible factors and degrees of a characteristic polynomial?
I made hand calculations for $n\le4$. It turns out that even with $V_n=1_n$, the factor $U_n$ is not unique. In other words, the factorisation problem is underdetermined. This is due to the fact that …