query: prove that $[F(\alpha):F]=p$ where $\alpha$ is a root of $x^p-a$
positive_passages.docid: 18336
positive_passages.text: $x^p-c$ has no root in a field $F$ if and only if $x^p-c$ is irreducible?
negative_passages.docid: 48275
negative_passages.text: $f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
negative_passages.docid: 250
negative_passages.text: An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root?
negative_passages.docid: 46844
negative_passages.text: Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$
negative_passages.docid: 7567
negative_passages.text: Degree of Field Extensions and $F(\alpha)$
negative_passages.docid: 46821
negative_passages.text: Finding roots in $\mathbb{Z}_p$
negative_passages.docid: 102464
negative_passages.text: Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
negative_passages.docid: 154507
negative_passages.text: If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
negative_passages.docid: 95594
negative_passages.text: Prove that a polynomial is irreducible or the field contains a $p$th root
negative_passages.docid: 148458
negative_passages.text: $x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
negative_passages.docid: 151356
negative_passages.text: Need Hints Prove "$((\neg \alpha \to \alpha) \to \alpha) $" Using Axiom 1,2,3 and MP and deduction theorem
negative_passages.docid: 46746
negative_passages.text: How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
negative_passages.docid: 65459
negative_passages.text: Roots of polynomials in field of prime characteristic p
negative_passages.docid: 6722
negative_passages.text: to show $f$ is a polynomial in $z$
negative_passages.docid: 118916
negative_passages.text: How do I prove that a polynomial F[x] of degree n has at most n roots
negative_passages.docid: 97454
negative_passages.text: Find the value of $\alpha-\beta$ if $g(x,y)=\alpha x+\beta y$ is a Hahn-Banach extension of $f$
negative_passages.docid: 122115
negative_passages.text: Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$