For every integer n, if n is greater than or equal to m, then n^5 - 1 is composite.
80144
Prove that $x-1$ divides $x^n-1$
33810
Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer
62043
the largest integer $n$ for which $n+5$ divivides $n^5+5$?
63383
Integers $n$ for which $|2^n + 5^n – 65|$ is a perfect square
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
119051
Show that only finitely many positive integers $n$ have the property that for all $m$ for which $1<m<n$ and $\text{gcd}(m,n) = 1$, $m$ is prime.
152577
Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
20705
On equations $m^2+1=5^n$
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
26087
Find all natural numbers $n > 1$ and $m > 1$ such that $1!3!5!\cdots(2n - 1)! = m!$
41354
Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
65757
Prove that $n! + k$ is a composite number
80242
Prove that $n^{2003}+n+1$ is composite for every $n\in \mathbb{N} \backslash\{1\}$
95141
$n^5-n$ is divisible by $10$?
154475
Prove that if $2^n - 1$ is prime, then $n$ is prime for $n$ being a natural number