A set of numbers ,
,
...,
(mod )
form a complete set of residues, also called a covering system, if they satisfy
for ,
1, ..., .
For example, a complete system of residues is formed by a base and a modulus if the residues in for , ..., run through the values 1, 2, ..., .
,
,
..., 
(mod 
)
form a complete set of residues, also called a covering system, if they satisfy
,
1, ..., 
.
For example, a complete system of residues is formed by a base 
and a modulus 
if the residues 
in 
for 
, ..., 
run through the values 1, 2, ..., 
.
