Find all primes $(p, q)$ such that $p^3 - q^5 = (p+q)^2$
87282
Diophantine equation involving prime numbers : $p^3 - q^5 = (p+q)^2$
10589
How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
97021
Do there exist two primes $p<q$ such that $p^n-1\mid q^n-1$ for infinitely many $n$?
110809
What can primes, except 2, 3, and 5, be congruent to $\pmod {30}$?
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
144814
If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?
146753
Find $x$ such that $(x^2 + 4x + 3)^x + (2x + 4)^x = (x^2 + 4x + 5)^x$
4402
Group of order $pqr$, $p < q < r$ primes
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
140412
If $p$ and $q$ are distinct primes such that $p|c$ and $q|c$, prove that $pq|c$
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
82016
Given $p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$, solve for $s$
152231
Computing the product of p/(p - 2) over the odd primes
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
10425
Suppose that $5\leq q\leq p$ are both prime. Prove that $24|(p^2-q^2)$.
113994
Let $p$ be a prime of the form $3k+2$ that divides $a^2+ab+b^2$ for some integers $a,b$. Prove that $a,b$ are both divisible by $p$.