modular arithmetic
Any system of arithmetic for integers which, for some given positive integer n, is equivalent to the set of integers being mapped onto the finite set {0, ... n} according to congruence modulo n, and in which addition and multiplication are defined consistently with the results of ordinary arithmetic being so mapped.
Noun
- Any system of arithmetic for integers which, for some given positive integer n, is equivalent to the set of integers being mapped onto the finite set {0, ... n} according to congruence modulo n, and in which addition and multiplication are defined consistently with the results of ordinary arithmetic being so mapped.
- The reader now has examined, in some detail, several specific modular arithmetics, namely, #92;mathbb#123;Z#125;#95;2,#92;mathbb#123;Z#125;#95;5,#92;mathbb#123;Z#125;#95;6,#92;mathbb#123;Z#125;#95;7,#92;mathbb#123;Z#125;...
- In this section we use two historical ciphers to introduce modular arithmetic with integers. Even though the historical ciphers are no longer relevant, modular arithmetic is extremely important in modern cryptography,...
- Hence for prime moduli, modular arithmetic is very similar to regular rational arithmetic with all four operations defined. - 1997, Robert E. Jamison, “Rhythm and Pattern: Discrete Mathematics with an Artistic...