A prime can be written as $a^2-ab+b^2$ if $p≡1$ (mod 3)
13904
$p = x^2 + xy + y^2$ if and only if $p \equiv 1 \text{ mod }3$?
158161
$\mathbb{Q}(\sqrt p_{1}+\sqrt p_{2})=\mathbb{Q}(\sqrt p_{1},\sqrt p_{2})$ for $p_{1},p_{2}$ primes.
96237
$1^2 + 2^2 + 3^2 + \cdots + (n-1)^2 \equiv 0$ mod n iff $n \equiv \pm 1$ mod 6
140198
Let $a$ be a quadratic residue modulo $p$. Prove that the number $b\equiv a^\frac{p+1}{4} \mod p$ has the property that $b^2\equiv a \mod p$.
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
23153
$\bmod p\!:\ x^2\equiv 1\iff x\equiv \pm1\ $ for prime $p$
58935
If $p$ and $p^2+8$ are both prime numbers, then $p^3+4$ is prime.
105442
Show that any prime divisor of $x^4+x^3+x^2+x+1$, with $x\in\mathbb{N}$, is $5$ or $1$ mod $5$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
834
If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$.
71110
Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
19700
Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
138259
Proof or disproof that every integer can be written as the sum of a prime and a square.
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.$