Positive integer multiples of an irrational mod 1 are dense
36546
For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
104234
What is the Hausdorff dimension of the set of irrationals on $\mathbb R^1$
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
132382
Showing a set is nowhere dense in $C([0,1])$
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
127816
Number theory proof mod p
87596
Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
121831
Proving that rational numbers are dense
35105
Density of ring of algebraic integers in $\mathbb C$
126199
Proof of $\pi$ not being a quadratic irrational number.
86988
Cardinality of the Irrationals
4972
Mod of numbers with large exponents [modular order reduction]
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
152172
Does there exist a positive irrational number $\alpha $, such that for any positive integer $n$ the number $\lfloor n\alpha \rfloor$ is not a prime?