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Modular Integer Numbers

Definition: The set of integers modulo m is the quotient set of Z with respect to congruence modulo m:

Z_m := Z/ = _m.

Proposition: Z_m has m elements each of which is represented by a natural number less than m, i.e.,

Zm = {[0]m, [1]m, [2]m, ..., [m-1]m}.