Prime cyclotomic field degree ($[\mathbb{Q}({\zeta }_p):\mathbb{Q}]=p-1$)

For a prime $p$, the cyclotomic polynomial of a primitive $p$th root of unity isIt is irreducible over $\mathbb{Q}$, so adjoining one root gives a field of degree $p-1$.

For an odd prime $p$ and a primitive $p$th root ${\zeta }_p$,