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 
would be a complete
residue system for 
(mod 6).
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.
