$(p-1)! \equiv - 1 \ \text{(mod $p$)}$.
2218
Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
153862
A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime.
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
124995
$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
139659
Find all $n$ with $\!\bmod n\!:\, a\,$ invertible $\Rightarrow a^{-1} \equiv a,\,$ i.e. $a^2\equiv 1$
92518
mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$
45171
How prove this $(p-1)!\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\right)\equiv 0\pmod{p^2}$
14724
For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
66861
Show that $11^{10} \equiv 1 (\mod 100)$
43567
Some hints for "If a prime $p = n^2+5$, then $p\equiv 1\mod 10$ or $p\equiv 9\mod 10$"
135986
Show if $a \equiv b \pmod{m}$ then $ac \equiv bc\pmod{mc}$
15314
Number of solutions to $x^n \equiv 1 \mod p$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$