Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 32 / 2 / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 20G / a / Solution

{title2=$[\mathbb Q(\zeta_p):\mathbb Q]=p-1$}

For a prime $p$, the <cyclotomic polynomial> of a primitive $p$th root of unity is
$$
\Phi_p(X)=1+X+\cdots+X^{p-1}.
$$
It is irreducible over $\mathbb Q$, so adjoining one root gives a field of degree $p-1$.

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 Incoming links: Prime cyclotomic field degree