If $p > 3$ is prime, then $12 $ divides $p^2 - 1$
15915
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
75733
Divisibility of prime numbers
121479
Why is $X^4+1$ reducible over $\mathbb F_p$ with $p \geq 3,$ prime
117167
$3^{n+1}$ divides $2^{3^n}+1$
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
63356
Can $x^{n}-1$ be prime if $x$ is not a power of $2$ and $n$ is odd?
118629
$p,q$ odd primes, $q\mid a^p-1\Rightarrow q\mid a-1$ or $\,2p\mid q-1$
29963
$6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
138193
Why is $\sqrt {12} = 2 \sqrt 3$?
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
68145
If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
100255
If a prime divides the hypotenuse of a primitive Pythagorean triple, then $p \equiv 1$ (mod 4)