Go backward to Modular Congruence Go up to Top Go forward to Modular Integer Numbers

Residue Class

Definition: The residue class of a modulo m is the set of all integer numbers that are congruent to a modulo m.

[a]m := [a] = m.

Proposition: [a]_m = {a+im: i in Z}, for every a in Z, m in Z_>0.

• = _m defines the [a]_m of our intuition.
• = _m also defines a suitable domain Z_m for modular arithmetic.