Prove that any prime p > 3 is either of the form 6k + 1 or of the form 6k + 5 for some integer k.
12365
Show that every prime $p>3$ is either of the form $6n+1$ or of the form $6n+5$
144592
how to prove the existence and uniqueness of the prime factorization of any natural number.
47162
Proving there are infinitely many primes of the form $a2^k+1.$
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
10425
Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
95111
Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.
25023
How do you prove that there are infinitely many primes of the form $5 + 6n$?
125855
Prove: The product of any three consecutive integers is divisible by $6$.
127816
Number theory proof mod p
5142
Infinitely many primes of the form $pn+1$
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
6918
Primes congruent to 1 mod 6
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
137715
If $[L:K]$ is prime, show that $L/K$ is a simple extension.
40968
show if $n=4k+3$ is a prime and ${a^2+b^2} \equiv 0 \pmod n$ , then $a \equiv b \equiv 0 \pmod n$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$