“Residue Class”的概念、定义、习题解题方法及翻译-数学辞典

单词

Residue Class

释义

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 eachclass, so in this case,

would be a Complete Residue System for

(mod 6), as would

, etc.

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.

See also Complete Residue System, Congruence, Cubic Number, Quadratic Reciprocity Theorem,Quadratic Residue, Residue (Congruence), Square Number

References

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 56 and 59-63, 1993.

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