$(n-1)! \equiv 0 \pmod n$, Wilson's Theorem version for non prime moduli
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
84746
elementary proof that infinite primes quadratic residue modulo $p$
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
47060
Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
44857
Why the $(n+1)$th prime number cannot exceed the smallest prime divisor of $p_1\dotsc p_n + 1$
82482
Proving an infinite number of primes of the form 6n+1
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
20980
Prove that $\frac{p^p-1}{p-1}$ is not prime if $p \equiv 1 \pmod 4$
119433
How to find modulo of large numbers like $9801\! \pmod {\!32}$
38876
$r! \equiv (−1)^k \pmod p$
27850
Find and prove a formula for $1\pmod{3}\cap 1\pmod{7}$.
52530
There exists a prime congruent to $m$ mod $p$
158684
How to solve and see resolution of $13^{53} \pmod 7$ using Fermat little Theorem?
27287
$-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$