Property of modular arithmetic. $a \bmod p = b \bmod p \iff p \uparrow |a-b|$
101385
Congruent iff Same Remainder (CISR) Confusion
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
96398
An integer $a \pmod m$ has inverse if and only if $\gcd(a,m)=1$?
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
75528
$x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
111555
Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$
138088
Diffie-Hellman key exchange: Why is $(g^{k_1} \bmod n )^{k_2} \bmod n \equiv (g^{k_2} \mod n)^{k_1} \bmod n$
94429
Alternative methods to prove that $Z_m$ is a field under addition and multiplication $\bmod\ m$ iff $m$ is a prime
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$
9806
$M$ finitely generated if submodule and quotient are finitely generated.
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
93820
Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
360
Modular exponentiation by hand ($a^b\bmod c$)
10105
Proving $\, a^b = (a\bmod n)^b\, \pmod{\!n}\ $ [Congruence Power Rule]
27287
$-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$
156089
Why is the associative property valid for modular arithmetic?