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Complete Residue System


A set of numbers a_0, a_1, ..., a_(m-1) (mod m) form a complete set of residues, also called a covering system, if they satisfy

 a_i=i (mod m)

for i=0, 1, ..., m-1. For example, a complete system of residues is formed by a base b and a modulus m if the residues r_i in b^i=r_i (mod m) for i=1, ..., m-1 run through the values 1, 2, ..., m-1.


See also

Congruence, Exact Covering System, Multiplicative Order, Reduced Residue System, Residue Class

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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.

Referenced on Wolfram|Alpha

Complete Residue System

Cite this as:

Weisstein, Eric W. "Complete Residue System." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CompleteResidueSystem.html

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