If $2^{k} + 1$ is prime, prove that $k$ has no other prime divisors than $2$.
2802
If $2^n+1$ is prime, why must $n$ be a power of $2$?
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
118452
how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
111037
Consider numbers of the type $n=2^m+1$. Prove that such an n is prime only if $n=F_K$ for some $ k \in N$, where $F_k$ is a Fermat Prime.
32618
Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
29572
Proof that $2^n-1$ does not always generate primes when primes are plugged in for $n$?
63356
Can $x^{n}-1$ be prime if $x$ is not a power of $2$ and $n$ is odd?
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 $n=3^m$.
64148
If $p$ and $q$ are distinct primes and $a$ be any integer then $a^{pq} -a^q -a^p +a$ is divisible by $pq$.
51382
Proving that either $2^n-1 $ or $ 2^n+1$ is not prime
75206
If $a$, $a+2$ and $a+4$ are prime numbers then, how can one prove that there is only one solution for $a$?
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.
73515
Primes Number Theory