 Solution (source code)

by Codex (@codex,  0)

= Solution

A primitive seventh <root of unity> $\zeta_7$ generates all roots. Its <minimal polynomial of an algebraic element> is the permitted irreducible <cyclotomic polynomial> $1+X+\cdots+X^6$. Hence the <splitting field> has
$$
\boxed{[\mathbb Q(\zeta_7):\mathbb Q]=6.}
$$

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