If $2^k - 1$ is prime then $k$ is prime, using $2^{m} -1 \vert 2^{mn} - 1$
102889
If $2^n - 1$ is prime from some integer $n$, prove that n must also be prime.
45037
Show $(2^m-1,2^n+1)=1$ if $m$ is odd
65511
Proving the following false: $f(x)=2x+1$ produces a prime number if and only if x is prime
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
142584
Confusion in proof that primes $p = 4k + 1$ are uniquely the sums of two squares
131476
consecutive prime power
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
20980
Prove that $\frac{p^p-1}{p-1}$ is not prime if $p \equiv 1 \pmod 4$
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
45341
$(m, m+2)$ is twin prime, iff $4((m-1)! + 1) \equiv -m \pmod {m(m+2)}$
43591
How to factor numbers that are the product of two primes
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
153294
What is the infinite product of (primes^2+1)/(primes^2-1)?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
113763
Let $p$,$\ q$ be prime numbers and $n\in \mathbb{N}$ such that $p \nmid n-1$. If $p \mid n^q-1$, then $q \mid p-1$.