query: Proving $L$ is the splitting field of $f(x) = \min_Q(ζ_7)$
positive_passages.docid: 16035
positive_passages.text: Irreducibility of $X^{p-1} + \cdots + X+1$
negative_passages.docid: 134840
negative_passages.text: Generators and relations for $\text{PSL}(2, \mathbb{F}_q)$
negative_passages.docid: 106401
negative_passages.text: Prove: $p-mq | f(m)$ where $m$ is any integer
negative_passages.docid: 124844
negative_passages.text: Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
negative_passages.docid: 41050
negative_passages.text: Degree of the splitting field of $ x^3-5 $ over $\mathbb{Q}$
negative_passages.docid: 78143
negative_passages.text: Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements
negative_passages.docid: 127796
negative_passages.text: Degree of field extension $F(x) / F(x^2 + 1 / x^2)$
negative_passages.docid: 3711
negative_passages.text: Finding the intermediate fields of $\Bbb{Q}(\zeta_7)$.
negative_passages.docid: 157426
negative_passages.text: Proving that:$\int_X f_n g \, d\mu \to \int_X fg \, d\mu$ for all $g$ in $\mathscr{L}^q (X)$
negative_passages.docid: 40400
negative_passages.text: Finding an isomorphism between $\mathbb{Z}[i]/(7)$ and $\mathbb{Z}[\sqrt{-2}]/(7)$
negative_passages.docid: 120985
negative_passages.text: Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
negative_passages.docid: 119305
negative_passages.text: Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
negative_passages.docid: 112556
negative_passages.text: When is $F(\sqrt c)$ a field?
negative_passages.docid: 103552
negative_passages.text: The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
negative_passages.docid: 45302
negative_passages.text: Finding the $\mathbb{Q}$-automorphisms of the splitting field of $x^p-2$ over $\mathbb{Q}$.
negative_passages.docid: 68774
negative_passages.text: Proving that $f(x)$ is less than or equal to $1+\pi/4$
negative_passages.docid: 108914
negative_passages.text: Splitting field of $x^n-a$ contains all $n$ roots of unity