query: $\zeta_5$ has degree $4$ over $\mathbb{Q}$ and $\zeta_7$ has degree $6$ over $\mathbb{Q}$
positive_passages.docid: 26233
positive_passages.text: $[K(\zeta_n):K]=\phi(n)$?
negative_passages.docid: 155771
negative_passages.text: Product of degree of two field extensions of prime degree
negative_passages.docid: 122952
negative_passages.text: Degree of extension is equal to linear combination of prime factor multiplicities with prime factor index coefficients in Dedekind domains
negative_passages.docid: 146969
negative_passages.text: Proving that every group of order $4$ is isomorphic to $\Bbb Z_4$ or $\Bbb Z^*_8$
negative_passages.docid: 57884
negative_passages.text: Number of monic irreducible polynomials of prime degree $p$ over finite fields
negative_passages.docid: 120699
negative_passages.text: Is $\mathcal{O}_{\mathbb{Q}(\sqrt{5})} = \mathbb{Z}[\phi]$?
negative_passages.docid: 28181
negative_passages.text: Sylow subgroups of $S_3$ and $S_4$
negative_passages.docid: 33338
negative_passages.text: Problem on $\operatorname{Hom}(\mathbb Z_6,R^*\oplus C^*)$
negative_passages.docid: 129239
negative_passages.text: Additive quotient group $\mathbb{Q}/\mathbb{Z}$ is isomorphic to the multiplicative group of roots of unity
negative_passages.docid: 24168
negative_passages.text: A characterisation of quadratic extensions contained in cyclic extensions of degree 4
negative_passages.docid: 4996
negative_passages.text: Proving $Gal(K/\mathbb{Q})$ is $D_4$.
negative_passages.docid: 95669
negative_passages.text: Solutions of $|z| = z^5$ in $\Bbb{C}$?
negative_passages.docid: 65558
negative_passages.text: Irreducible in $\mathbb{Z}[\sqrt{-5}]$
negative_passages.docid: 156909
negative_passages.text: $\Bbb{Z}_{26} \rtimes_{\alpha} \Bbb{Z}_{5} \cong \Bbb{Z}_{26} \times \Bbb{Z}_{5}$ as groups.
negative_passages.docid: 622
negative_passages.text: Galois Group of $\sqrt{2+\sqrt{2}}$ over $\mathbb{Q}$
negative_passages.docid: 84893
negative_passages.text: Solutions of the equations of the degree 5 and more
negative_passages.docid: 127814
negative_passages.text: Number of elements in the quotient ring $\mathbb{Z}_6 [x]/\langle 2x +4\rangle$