Show that exists $m, n \in \mathbb{Z}$ such that $|m+n \sqrt{2}|<\frac{1}{10}$.
29965
Proving that $m+n\sqrt{2}$ is dense in $\mathbb R$
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
55582
How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?
109305
Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
26011
To show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$ is the following adequate?
513
If n is an odd integer, show there exists a positive integer k such that 2^k mod n = 1.
90962
For positive integers $m,n$ if $\sqrt 7 - \frac{m}{n} > 0$ then prove that $\sqrt 7 - \frac{m}{n} > \frac{1}{{mn}}$
6582
Prove the existence of the square root of $2$.
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
91113
$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
53857
Showing $\sup \{ \sin n \mid n\in \mathbb N \} =1$
82636
Maybe is right $\frac{n^2 + 1}{4k + 3} \notin \mathbb{Z}, n, k \in \mathbb{N}^{+}$
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.
148163
Show that if m/n is a good approximation of $\sqrt{2}$ then $(m+2n)/(m+n)$ is better