How to show $\mathbb{Z} + \alpha \mathbb{Z}$ not closed for irrational $\alpha$?
13550
For an irrational number $\alpha$, prove that the set $\{a+b\alpha: a,b\in \mathbb{Z}\}$ is dense in $\mathbb R$
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
32848
Prove that the product of a non-zero rational and irrational number is irrational.
56464
Proving the irrationality of $e^n$
136855
Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
30192
How far are the $p$-adic numbers from being algebraically closed?
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
64885
Irrational and rational sequence proof
57639
Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
122759
Show $2+\alpha$ is a primitive root of $\mathbb{F}_{25}$.
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
151786
Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
91736
Explicit homeomorphism between open and closed rational intervals?
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
142168
can we a prove ⊢ (α → α) → (α → α)
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$