 TOPICS # Residue Class

The residue classes of a function mod are all possible values of the residue . For example, the residue classes of (mod 6) are , since are all the possible residues.

A complete residue system is a set of integers containing one element from each class, so would be a complete residue system for (mod 6).

The residue classes prime to form a group under the binary multiplication operation (mod ), where is the totient function (Shanks 1993) and the group is classed a modulo multiplication group.

Complete Residue System, Congruence, Cubic Number, Quadratic Reciprocity Theorem, Quadratic Residue, Reduced Residue System, Residue, Square Number

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## References

Nagell, T. "Residue Classes and Residue Systems." §20 in Introduction to Number Theory. New York: Wiley, pp. 69-71, 1951.Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 56 and 59-63, 1993.

Residue Class

## Cite this as:

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