Proving $\{a+b\sqrt{-7}, a,b\in\frac{\mathbb{Z}}{2}\}$ is a euclidean domain
11935
Is $\mathbb{Z} \left[ \frac{1+i \sqrt{7}}{2} \right]$ euclidean?
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
17161
Can anyone make me understand in simple language why the second condition for being an Euclidean domain is superfluous?
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
41558
Prove that $\frac4{abcd} \geq \frac a b + \frac bc + \frac cd +\frac d a$
95863
Describe the units in $\mathbb{Z}[\sqrt{-d}]$
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
54957
The necessary and sufficient condition for a unit element in Euclidean Domain
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
112043
Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
3317
Subgroup generated by $2$ and $7$ in $(\mathbb Z,+)$
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
111291
Galois group of $\mathbb Q(\sqrt{4+\sqrt 7})/\mathbb Q$
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
68389
Proving $ \frac{(a-b)^2}{8a}\leqslant\frac{a+b}{2} - \sqrt{ab} \leqslant\frac{(a-b)^2}{8b}$ when $ 0<b\le a$