Modular arithmetic. $(-1)^rr! \equiv 1 \pmod p$, then $(p-r-1)! \equiv -1 \pmod p$
7932
$(p\!-\!1\!-\!h)!\,h! \equiv (-1)^{h+1}\!\!\pmod{\! p}\,$ [Wilson Reflection Formula]
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
97196
$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
22962
How to show $\binom{2p}{p} \equiv 2\pmod p$?
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
41673
Solve congruence system $\ x\equiv m_i-1 \pmod{m_i}\,$ for $\,i = 1,\ldots, k$
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
42754
Modular arithmetic: division, fractions, solving linear congruences
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
68635
When is $2$ a quadratic residue mod $p$?
62382
I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
78356
How to prove ${n \choose p} \equiv\left\lfloor \frac{n}{p} \right\rfloor\pmod p$
22029
Solving modular arithmetic questions
134450
Chinese Remainder Theorem $\ x\equiv m_k-2\pmod{m_k}$
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
18634
Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$