Prove $a^{(p-1)!}\equiv1 \pmod p$.
4972
Mod of numbers with large exponents [modular order reduction]
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
44729
Prove $g$ is a generator if $g^q=1 \pmod p$
20980
Prove that $\frac{p^p-1}{p-1}$ is not prime if $p \equiv 1 \pmod 4$
63661
integers $n$ such that $(n-1)!+1$ is a power of $n$
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
134348
When is $(p - 1)! + 1$ a power of $p$?
38805
Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$.
144017
How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$
32463
$ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$
100426
Let $a$ and $b$ be integers. Show that if $a \equiv b \pmod{p}$ for every prime $p$, then $a = b$.
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
103732
Proving that for $n \equiv 0 \pmod{2}$, we get ${n \choose 0} < {n \choose 1} <\ldots< {n \choose n/2-1}<{n\choose n/2}$ etc.
6332
If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$