## Quick Reference

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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