Proving that $a=2$ and $n$ is a prime given $p$ is a prime in $p= a^n - 1$
30134
For $a,n \in \Bbb N$, how to prove if $a^n-1$ is prime then $a=2$ and $n$ is prime?
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
103360
Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
29572
Proof that $2^n-1$ does not always generate primes when primes are plugged in for $n$?
39915
Let $n$ be an integer such that if $d | n$ then $d + 1 | n + 1.$ Show that $n$ is a prime number
119282
If $a_1,a_2,\ldots, a_n$ are distinct primes, and $a_1=2$, and $n>1$, then $a_1a_2\cdots a_n+1$ is of the form $4k+3$.
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
157711
Number Theory: Prove that $m | \phi(a^m - 1)$
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$