Prove n is a perfect square if and only if $n^7$ is a perfect square, n $\in$ natural numbers
82938
$\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.
118538
Find all integers $x$ such that $x^2+3x+24$ is a perfect square.
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
145676
Percentage of natural numbers that are perfect squares?
20964
Proof that $n^2 < 2^n$
60615
Product of $5$ consecutive integers cannot be perfect square
55266
Prove that $(n+1)^{n-1}<n^n$
24403
Prove that $ n < 2^{n}$ for all natural numbers $n$.
136366
Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.
138548
For what pair of integers $(a,b)$ is $3^a + 7^b$ a perfect square.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
134
Prove that the expression is a perfect square
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
59782
Are there any $n$ for which $ n^4+n^3+n^2+n+1$ is a perfect square?
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$