Complete Residue System

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, ..., .

REFERENCES:

Guy, R. K. "Covering Systems of Congruences." §F13 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 251-253, 1994.

Nagell, T. "Residue Classes and Residue Systems." §20 in Introduction to Number Theory. New York: Wiley, pp. 69-71, 1951.