$p$ is an odd prime number where $p=3k+1\Longleftrightarrow\exists a,b\in\Bbb Z^+$ such that $p=a^2+ab+b^2$
6918
Primes congruent to 1 mod 6
56328
Find p is the prime number which $\frac{p+1}{2}$ and $\frac{p^2+1}{2}$ both are square number.
126893
A group of order 2p (p prime) and other conditions - prove abelian.
146512
Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
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 $p$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
100984
Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
60780
Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.
5142
Infinitely many primes of the form $pn+1$
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
86594
If $x^2 \equiv y^2 \pmod {p^r}$, where $p$ is an odd prime not dividing $x$ or $y$ then $x \equiv \pm y \pmod {p^r}$
33714
$p$ prime, $p\mid a^k \Rightarrow p^k\mid a^k$
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
131488
Show that $p^3+4$ is prime
156607
Show that $L_p =\frac{1^p+2^p+3^p+...+(p-1)^p}{p}$ is an integer and generalize the integer for all odd integers p
156272
Unique pair of positive integers $(p,n)$ satisfying $p^3-p=n^7-n^3$ where $p$ is prime