Solutions of $x^2+3y^2=p$ for $p$ prime
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
69874
Are there any integer solutions to $a^3=b^2$?
87282
Diophantine equation involving prime numbers : $p^3 - q^5 = (p+q)^2$
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
152591
For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?
131488
Show that $p^3+4$ is prime
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
146512
Prove that for every prime number $p>3$, $4p^2+1$ can be written as the sum of three square numbers
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
102204
Factoring product of two primes from solutions of congruence
63194
Find all integer solutions to $x^2-2y^2=1$
77595
Number of solutions of $x_1 + 2x_2 + 3x_3 + \cdots + n x_n = p$
23099
Verifying that the ideal $(x^3-y^2)$ is prime
45454
Pairs of $(p,q)$ such that $p^2 + 1 = 2 q^2$?
158933
Rational solutions of $y^2 = x^3 - x$
150085
Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$
50760
Solutions to $y^2 = x^3 + k$?