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Each number in modular number crunching system has an additive counterpart, which is its opposite. The summation of the number and its opposite results to 0 modulo n. In the case of a + b ≡ 0 (mod n) Zn, a and b are the polar opposites of one another [5, 7].

Furthermore, a number may theoretically have a multiplicative inverse known as a reciprocal. The whole number multiplied by its inverse is compatible with 1 modulo n. In the case of a × b ≡ 1(mod n) Zn, a and b are reciprocals of one another [5, 7].

In cryptography, two additional sets are sometimes used: Zp and Zp*, where p is a prime integer. Each member of Zp has its corresponding opposite and reciprocal, but the zero does not have a reciprocal. Each member of Zp* is guaranteed to have both an opposite and a reciprocal [5, 7].