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Complete Residue System

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


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

Congruence, Exact Covering System, Haupt-Exponent, Modulo 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.




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



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