Prove that if $p = 2^{m}+ 1$ is prime, then $m$ is a power of $2$
2802
If $2^n+1$ is prime, why must $n$ be a power of $2$?
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
109532
Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
26514
Prove that if $n$ is a composite, then $2^n-1$ is composite.
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
52530
There exists a prime congruent to $m$ mod $p$
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
20881
Prove that if $p$ and $q$ are distinct primes such that $pq\mid n^2$ then $pq\mid n$.
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
127816
Number theory proof mod p
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
98871
How to prove that if a prime divides a Fermat Number then $p=k\cdot 2^{n+2}+1$?
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$