Why do the modular multiplicative inverse of an integer $a$ always exists when it is coprime with the modulus?
946
How to find solutions of linear Diophantine ax + by = c?
83753
Why $\,p \cdot (p^{-1} \mod q) + q \cdot (q^{-1} \mod p) = pq + 1$?
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
152299
Proving $a^{n-1} \equiv 1 \mod n $ when n is not prime.
103695
Prove Inverses not need be Unique if Associativity fails
19071
solution set for congruence $x^2 \equiv 1 \mod m$
81687
What is the importance of Modular arithmetic in cryptography?
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
16700
Modular reduction of fractions
114346
Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
42332
Existence of multiplicative inverse in field $\mathbb{Q}(\sqrt{d})$
93820
Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
117484
Why is $c+q$ still a primitive root modulo $q$?
138279
Multiplicative order and powers
42754
Modular arithmetic: division, fractions, solving linear congruences
38727
Modular Exponentiation and Primes
76032
Prove that if m is a square integer then m is neither congruent to 2 modulo 5 nor congruent to 3 modulo 5