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 .