Prove that there are infinitely many primes p, such that the congruence $x^7$ + $3x^5 + 1 \equiv 0 \mod p$ has a solution
75528
$x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
38379
Showing that $e^z=z$ has infinitely many solutions
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
15314
Number of solutions to $x^n \equiv 1 \mod p$
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
131395
Solving linear congruence $2x + 11 \equiv 7 \pmod 3$
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
84746
elementary proof that infinite primes quadratic residue modulo $p$
81723
Infinitely many primes proof using Euler's totient
2147
Different ways to prove there are infinitely many primes?
108035
solving diophantine equations using congruences
126725
If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...
16621
Help understand the proof of infinitely many primes of the form $4n+3$
98468
Are there infinitely many primes of the form $n!+1$?
84641
Infiniteness of set of primes such $f$ have root $\mod p$
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.