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.

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1999-05-26