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Residue class

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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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