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.
