For which prime numbers $p$ does the congruence $x^2 + x + 1 \equiv 0 \pmod{p}$ have solutions?
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
143754
Finding the solution of the congruence $4x\equiv16\pmod{26}$
75528
$x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
46028
Show that the solution for the Diophantine equation $x^2 - y^2 = N$ is unique if and only if $|N|$ or $\frac{|N|}{4}$, respectively, is $1$ or prime.
136856
Diophantine equation with a prime number
56803
Finding solutions to congruence equations
38748
There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also prime numbers
34617
Number Theory: which primes are a sum of two squares?
95162
For a odd prime $p, \exists a,b$ such that $a^2 + ab + b^2 \equiv 0 \pmod{p} \iff \exists x,y $ such taht $x^2 + xy + y^2 = p$?
58114
For which primes p is $p^2 + 2$ also prime?
77024
Find the number of solutions of $x^2=x\mod m$ for any integer $m$
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
14809
Existence & uniqueness of solutions of linear congruences $\ cx\equiv b\pmod m$
106271
Solutions of Diophantine equations in Natural numbers
42032
Find all solutions to $x^2\equiv 1\pmod {91},\ 91 = 7\cdot 13$
75206
If $a$, $a+2$ and $a+4$ are prime numbers then, how can one prove that there is only one solution for $a$?
133925
Find All Solutions to System of Congruence