Applying Wilson's Theorem to Prove a Congruence
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
65873
A proof for Atiyah-Macdonald Exercise I.21.iii
10966
gcd and lcm from prime factorization proof
130300
Proof that every quadratic residue has two roots, modulo a prime
111165
Prove the converse of Wilson's Theorem
61825
Congruence class $[a]$ modulo $m$, $\gcd(x, m) = \gcd(a, m)$
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
84746
elementary proof that infinite primes quadratic residue modulo $p$
84501
Proof involving Cyclic group, generator and GCD
36713
Solving multiple congruences by CRT = Chinese Remainder Theorem
74523
Proof by Cases involving divisibility
137175
Fermat's little theorem proof by Euler
38727
Modular Exponentiation and Primes
11989
$ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form]
8481
System of congruence relations
18245
How to check if a system of congruence is solvable?
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$