modulo n, addition

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The word ‘modulo’ means ‘to the modulus’. For any positive integer n, let S be the complete set of residues {0, 1, 2,…, n−1}. Then addition modulo n on S is defined as follows. For a and b in S, take the usual sum of a and b as integers, and let r be the element of S to which the result is congruent (modulo n); the sum a+b (mod n) is equal to r. Similarly, multiplication modulo n is defined by taking ab (mod n) to be equal to s, where s is the element of S to which the usual product of a and b is congruent (modulo n). For example, addition and multiplication modulo 5 are given by the following tables:

Subjects: Mathematics.

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