Discreteness of $\{ a+b\sqrt2 \mid a,b \in \Bbb N \}$ in $\Bbb R$
26256
Characterizing Dense Subgroups of the Reals
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
10236
Show that $a^n \mid b^n$ implies $a \mid b$
40848
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
44496
Norm $N$ on $\Bbb Z[\sqrt d]$ is multiplicative, $N(x)$ prime $\Rightarrow x$ irreducible
14210
Fibonacci divisibilty properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
78031
$c\mid a,b\iff c\mid\gcd(a,b)$ [GCD Universal Property]
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
82843
Subgroups of $\Bbb{R}^n$ that are closed and discrete
96630
Let a and b be real numbers such that 0  \sqrt{ab} > \frac{2ab}{a + b}$
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
90276
Is $\sqrt{2}\in{\Bbb Z}[\sqrt{2}+\sqrt{3}]$ true?
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
37219
Quadratic Integers in $\mathbb Q[\sqrt{-5}]$