$2^n + 1$ is prime $ \implies n$ is a power of $2$
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
63661
integers $n$ such that $(n-1)!+1$ is a power of $n$
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
134348
When is $(p - 1)! + 1$ a power of $p$?
37315
not both $2^n-1,2^n+1$ can be prime.
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
122612
An integer is a $n$'th power if that holds true for all moduli.
62982
Prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$
68328
Infinitely many $n$ such that $2^n-n$ is divisible by a prime
47162
Proving there are infinitely many primes of the form $a2^k+1.$