query: Prove that $E=\Bbb Q(\sqrt[d]{a})$
positive_passages.docid: 145140
positive_passages.text: Subfield of $\mathbb{Q}(\sqrt[n]{a})$
negative_passages.docid: 29935
negative_passages.text: If $a, b, c, d>0$ and $abcd=1$ prove that an inequality holds true
negative_passages.docid: 41558
negative_passages.text: Prove that $\frac4{abcd} \geq \frac a b + \frac bc + \frac cd +\frac d a$
negative_passages.docid: 109109
negative_passages.text: Show that $E(XE[X|G])=E[(E[X|G)^2]$
negative_passages.docid: 130854
negative_passages.text: Constructing example showing $\mathbb{E}(X^{-1})=(\mathbb{E}(X))^{-1}$
negative_passages.docid: 90796
negative_passages.text: Inequality Regarding e
negative_passages.docid: 138962
negative_passages.text: $X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.
negative_passages.docid: 73277
negative_passages.text: Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
negative_passages.docid: 57166
negative_passages.text: Showing that $\Bbb R[x] / \langle x^2 + 1 \rangle$ is isomorphic to $\Bbb C$ question
negative_passages.docid: 56928
negative_passages.text: $\dfrac{pq}{r}+\dfrac{qr}{p}+\dfrac{pr}{q}\in\Bbb Z\,\Rightarrow\, \dfrac{pq}{r},\dfrac{qr}{p},\dfrac{pr}{q}\in\Bbb Z$
negative_passages.docid: 90276
negative_passages.text: Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
negative_passages.docid: 31724
negative_passages.text: How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
negative_passages.docid: 144819
negative_passages.text: Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$
negative_passages.docid: 111406
negative_passages.text: Proving that a definition of e is unique
negative_passages.docid: 118195
negative_passages.text: How does one prove that $e$ exists?
negative_passages.docid: 14013
negative_passages.text: How to prove that $\lim \frac{1}{n} \sqrt[n]{(n+1)(n+2)... 2n} = \frac{4}{e}$
negative_passages.docid: 108550
negative_passages.text: Elements of $\mathbb Q(2^{1/3})$