Congruence Class is the set of all integers that are congruent to . Operations § Addition - Subtraction: Multiplication: Theorems § A pair of congruence classes and are zero divisors if and only if both and are non-zero, but . If gcd(a, n) then has (and is) a zero-divisor. A pair of congruence classes and are inverses if and only if . A congruence class with an inverse is called ”invertible“. is invertible if and only if .