## Quick Reference

*m* be some given but fixed positive integer and let *a* and *b* be arbitrary integers. Then *a* is congruent to *b* modulo *m* if and only if (*a* - *b*) is divisible by *m*. It is customary to write this as *a* ≡ *b* (modulo *m*) One of the most important uses of the congruence relation in computing is in generating random integers. A sequence *s*_{0},*s*_{1},*s*_{2},… of integers between 0 and (*m* - 1) inclusive can be generated by the relation *s*_{n}_{+1} ≡ *as** _{n}* +

*c*(modulo

*m*) The values of

*a*,

*c*, and

*m*must be suitably chosen.

*a* ≡ *b* (modulo *m*)

*s*_{0},*s*_{1},*s*_{2},…

*s*_{n}_{+1} ≡ *as** _{n}* +

*c*(modulo

*m*)

*R* (defined on a set *S* on which a dyadic operation ° is defined) with the property that whenever *x R u* and *y R v* then (*x* ° *y*) *R* (*u* ° *v*) This is often referred to as the **substitution property**. Congruence relations can be defined for such algebraic structures as certain kinds of algebras, automata, groups, monoids, and for the integers; the latter is the congruence modulo *m* of def. 1.

*x R u* and *y R v*

then (*x* ° *y*) *R* (*u* ° *v*)

*Subjects:*
Computing.

## Related content in Oxford Index

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.