If $n^x\in\Bbb Z,$ for every $n\in\Bbb Z^+,$ then $x\in\Bbb Z$
102039
If any integer to the power of $x$ is integer, must $x$ be integer?
138026
To show that $n!f(x) \in \mathbb{Z}[x]$
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
65391
Prove by induction. $n \in \mathbb N$.
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
17519
Let $z \in\Bbb{C}^{\times}$ such that $|z^3+\frac{1}{z^3}|\leq 2$. Prove that $|z+\frac{1}{z}|\leq 2$.
54554
If a product of relatively prime integers is an $n$th power, then each is an $n$th power
48211
When is $(a+b)^n \equiv a^n+b^n$?
77735
When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$
50880
Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
122914
An integer $n$, such that $nx = 0$, where $x$ belongs to the quotient group $\Bbb Q/\Bbb Z$
127720
Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
124240
Inductive proof of $\,9 \mathrel| 4^n+6n-1\,$ for all $\,n\in\Bbb N$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
7105
Prove that $\prod\limits_{i=1}^n \frac{2i-1}{2i} \leq \frac{1}{\sqrt{3n+1}}$ for all $n \in \Bbb Z_+$