Find all primes $p$ and $q$ such that $pq\mid 2^p+2^q$.
137230
Find all pairs of primes $p,q$ such that $pq \mid 2^p +2^q$
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
103360
Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime
5978
Prove that there exists only one prime number of the form $p^2−1$ where $p≥2$ is an integer
58182
How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
115726
For $p,q$ prime and $p \neq q$ show that $C_p \times C_q \cong C_{pq}$
65826
Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.
10425
Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
139930
Find all polynomials $p$ such that $p(x^2)=p(x)p(x+1)$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
120554
highest power of prime $p$ dividing $\binom{m+n}{n}$
73515
Primes Number Theory
112120
Find all primes of the form $2^{2^n} + 5$ for a nonnegative integer n
54359
Odd Primes Problem Proof
33714
$p$ prime, $p\mid a^k \Rightarrow p^k\mid a^k$
130846
Prove or disprove: If $a \in \mathbb{Z}$, $a > 0$, and $p$ is a prime such that $p^4 \mid a^3$, then $p^2 \mid a$.
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$