## Residue Class

The residue classes of a function mod are all possible values of the Residue . For example, the residue classes of (mod 6) are , since are all the possible residues. A Complete Residue System is a set of integers containing one element from each class, so in this case, would be a Complete Residue System for (mod 6), as would , etc.

The residue classes prime to form a Group under the binary multiplication operation (mod ), where is the Totient Function (Shanks 1993) and the Group is classed a Modulo Multiplication Group.