Definition (Congruence)
Let a,b∈Z, we say a is congruent to b modulo m if m∣a−b or a=b+km for some k∈Z. We represent this relationship using the following notation a≡b (mod m)
Theorem (Solution to Congruence)
The congruence ax≡b(modm) where d=gcd(a,m) and d∣b has a solution x≡a1−1b1(modm/d)where a1=da,b1=db.