If $p$ and $p^2+2$ prime, then $p^3+2$ prime.
66216
Squares, Cubes and Prime numbers
135586
Prove that the preimage of a prime ideal is also prime.
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
34692
Prove if $ p$ is a prime of the form $3n+1$, then $p$ is also of the form $6m+1$
124995
$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
146512
Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
32618
Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
126893
A group of order 2p (p prime) and other conditions - prove abelian.
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
19979
Why does $p^2+8$ prime imply $p^3+4$ prime
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
52530
There exists a prime congruent to $m$ mod $p$