Difference between revisions of "Residue class"

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In [[modular arithmetic]], 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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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.
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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 $a$ in modulo $n$ is the unique value of $0\leq r \leq n-1$ such that $a=kn + r$. In the context of division, a residue is simply a remainder.

A residue class is a complete set of integers that are congruent modulo $n$ for some positive integer $n$. In modulo $n$, there are exactly $n$ different residue classes, corresponding to the $n$ possible residues $\{0,1,2,3,... n-2, n-1\}$

Each residue class contains all integers in the form $kn + r$ where $r$ is the corresponding residue.

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