Let $n$ be contained in $\mathbb N$. Show that $ n^{1/2}$ is either an integer or it is irrational.
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
64885
Irrational and rational sequence proof
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
4750
Show that for any positive integer n, $(3n)!/(3!)^n$ is an integer.
36546
For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$
33786
Proof that a certain fraction is always an integer
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
87596
Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
42444
Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
27889
If the set of odd numbers is a subset of $\mathbb N$ then surely it is smaller than $\mathbb N$
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
43940
Showing that $n$ is pseudoprime to the base $a$
131634
Prove the irrationality of $0.235711131719...$