Prove that $\Bbb Z[\sqrt{2}, \sqrt{3}]$ does not equal $\Bbb Z[\sqrt{2} + \sqrt{3}]$.
90276
Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
8589
$\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
101448
Is $\sin^2(z) + \cos^2(z)=1$ still true for $z \in \Bbb{C}$?
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
113359
Proving that $x^2 + 4$ is not divisible by $3$
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
104300
Help justifying that $\mathbb Q(\sqrt[3]{2})$ is not a splitting field over $\mathbb Q$.
125668
A proof that BS(1,2) is not polycyclic
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
67605
Different proof that $\sqrt{2}$ is irrational
112043
Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
137285
Prove $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not isomorphic to $\mathbb{Z}_4$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
104562
Prove that $\mathbb{Z}$ is not isomorphic to additive group of any vector space over any field.
136868
Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$