If $n^{\alpha}$ is an integer for every $n\in\mathbb N$, is $\alpha$ a nonnegative integer?
981
If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
65391
Prove by induction. $n \in \mathbb N$.
83595
Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
129647
$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$
48211
When is $(a+b)^n \equiv a^n+b^n$?
104920
Can we find positive integers $a$ and $k \geq 2$ with $2^n - 1 = a^k$?
56574
For any integer $a,b$ let $N_{a,b}$ denote the number of positive integer $x<1000$ satisfying $x= a( mod\;27)$ and $x=b(mod\;37)$. Then
29084
Largest integer that can't be represented as a non-negative linear combination of $m, n = mn - m - n$? Why?
102039
If any integer to the power of $x$ is integer, must $x$ be integer?
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
133406
$n^a$ integral for all integer $n$ implies $a$ integral
82739
Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic?
97878
Are there uncountably many surjections from $\mathbb N$ to $\mathbb N$?
67208
Can we say that there exist an integer $n$ such $A+nB$ invertible?
44706
Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$