Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
37219
Quadratic Integers in $\mathbb Q[\sqrt{-5}]$
69046
Proof of $\mathbb{Q}$ is not cyclic
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
16163
Show $\mathbb{Q}(\sqrt{2},\sqrt{3})$ is a simple extension field of $\mathbb{Q}$.
22224
Define $S\equiv\{ x\in \mathbb{Q}\mid x^2<2\}$. Show that $\sup S=\sqrt{2} $.
8589
$\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
58182
How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
115282
Showing that $\mathbb Q(\sqrt{17})$ has class number 1
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
149661
For $n=pq$, show that there exist $\alpha, \beta \in Z_n^*$ such that $\alpha, \beta \notin (Z_n^*)^2$ and $\alpha \cdot \beta \notin (Z_n^*)^2$.
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
77240
Show that $4 + \sqrt{10}$ is not prime in $\mathbb{Z}\bigl [\sqrt{10}\bigr]$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$