Let $K=\mathbb{Q}(\sqrt[3]{2})$ then $U(K)=\{\pm (\sqrt[3]{2} -1)^n : n \in \mathbb{Z}\}$
68915
What are the units in $\mathbb{Z}[\root 3 \of 2]$?
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
86807
The units of $\mathbb Z[\sqrt{2}]$
17601
How to prove that if $a\equiv b \pmod{kn}$ then $a^k\equiv b^k \pmod{k^2n}$
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
22224
Define $S\equiv\{ x\in \mathbb{Q}\mid x^2<2\}$. Show that $\sup S=\sqrt{2} $.
46730
How to show $\mathbb{Q}(\alpha^{4})=\mathbb{Q}(\alpha)$?
74318
Find the nilpotents in $\mathbb{Z}_3[x]/(x^2-1)$
85977
Show that if $\sqrt{a}+\sqrt{b}\neq 0$, then $\mathbb{Q}(\sqrt{a}+\sqrt{b}) = \mathbb{Q}(\sqrt{a},\sqrt{b}), \forall a,b\in\mathbb{Q}$
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
78985
Prove that: $\sqrt{2\sqrt{3\sqrt{4\cdots\sqrt{n}}}}<3,\,\forall n\in\mathbb N.$
138501
Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
23048
The ring $\mathbb Z[\sqrt{-2}]= \{a+b\sqrt{-2} ; a\in \mathbb Z,b\in \mathbb Z \}$ has a Euclidean algorithm
103763
Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$
45627
Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$