Difference between revisions of "Residue class"
Chickendude (talk | contribs) (Added page for Residue class) |
Chickendude (talk | contribs) (Added information about residues as well) |
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| − | In [[modular arithmetic]], a residue | + | In [[modular arithmetic]], a residue of an integer <math>a</math> in modulo <math>n</math> is the unique value of <math>0\leq r \leq n-1</math> such that <math>a=kn + r</math>. In the context of division, a residue is simply a remainder. |
| − | Each residue class contains integers in the form <math>kn + r</math> where <math>r</math> is the corresponding residue. | + | A residue class is a complete set of integers that are congruent modulo <math>n</math> for some positive integer <math>n</math>. In modulo <math>n</math>, there are exactly <math>n</math> different residue classes, corresponding to the <math>n</math> possible residues <math>\{0,1,2,3,... n-2, n-1\}</math> |
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| + | Each residue class contains all integers in the form <math>kn + r</math> where <math>r</math> is the corresponding residue. | ||
Latest revision as of 18:25, 27 April 2008
In modular arithmetic, a residue of an integer 
in modulo 
is the unique value of 
such that 
. In the context of division, a residue is simply a remainder.
A residue class is a complete set of integers that are congruent modulo for some positive integer . In modulo , there are exactly different residue classes, corresponding to the possible residues 
Each residue class contains all integers in the form 
where 
is the corresponding residue.
