Proving that $(p-3)!+2^{p-2} \equiv 0 \ (\mathrm{mod} \ p)$ if $p \geq 3$ is prime
7932
$(p\!-\!1\!-\!h)!\,h! \equiv (-1)^{h+1}\!\!\pmod{\! p}\,$ [Wilson Reflection Formula]
23099
Verifying that the ideal $(x^3-y^2)$ is prime
35167
Prove congruence using fermat's thm
50663
prove or disprove: For a prime number p, there is a positive integer n such that $p+1 $= $n^2$ if and only if $ p = 3.$
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
75318
How do you prove that a prime is the sum of two squares iff it is congruent to 1 mod 4?
136279
Infinitely many primes $\equiv 3 \mod 4$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
11989
$ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form]
39943
Proving $\mathrm e <3$
110752
$g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
111967
Let $p$ be a prime number. Prove that there exists $x∈Z$ for which $p|x^2−x+ 3$ if and only if there exists $y∈Z$ for which $p|y^2−y+ 25$.
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
11564
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})=\mathbb{Q}(\sqrt{p}\sqrt[3]{q})$ for distinct prime $p,q$
146851
Prove that $-3$ is a quadratic residue mod an odd prime $>3$ if and only if $p$ is of the form of $6n+1$
1702
Proving that there are infinitely many primes with remainder of 2 when divided by 3