$n^x$ are rationals for all positive integers n, show $x$ must be an integer.
981
If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.
98440
Show that any non-negative rational integer may be written as the sum of two squares if it is of the form....
90076
Prove that every positive integer $n$ is a unique product of a square and a squarefree number
85895
Proving all rational numbers including negatives are countable
115799
Proving $x^{\log n} = n^{\log x}$
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
68139
Show that the set of polynomials with rational coefficients is countable.
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
38851
To find the probability whether $X$ is rational
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
123195
Prove by induction that a^n+a^-n is an integer.
5595
$x^y = y^x$ for integers $x$ and $y$
130093
Prove by Induction : $n < 2^n$
102039
If any integer to the power of $x$ is integer, must $x$ be integer?
122612
An integer is a $n$'th power if that holds true for all moduli.