If $m^x$ an integer for all naturals $m$ then $x$ and integer
981
If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
91451
find all positive integer $m,n$
89792
Let $x,y$ be positive real numbers. Then $x<y$ iff $x^n<y^n$ for all $n\in \mathbb{N}$
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$
145397
How to prove that for every $i$, $a_i = i$
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
123195
Prove by induction that a^n+a^-n is an integer.
151153
Prove $\frac{a(a^2+2)}{3}$ is an integer for all integer $a\geqslant 1$
140140
An identity which applies to all of the natural numbers
33877
What does $2^x$ really mean when $x$ is not an integer?
8884
Find all natural numbers $n$ and $m$ for which $n^m=(n-1)!+1$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
148647
If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
68976
Given real numbers: define integers?