prove that if $a^n+1$ is prime then $a$ is even and $n=2^k$
42885
Fermat primes relation to $2^n+1$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
33714
$p$ prime, $p\mid a^k \Rightarrow p^k\mid a^k$
83738
Prove $(k,n+k)=1$ iff $(k,n)=1$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
29462
Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$
65757
Prove that $n! + k$ is a composite number
23544
Complete induction proof that every $n > 1$ can be written as a product of primes
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
30374
If $n\in\mathbb N$ and $4^n+2^n+1$ is prime, prove that there exists an $m\in\mathbb N\cup\{0\}$ such that $n=3^m$.
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$