modular arithmetic
Sign in to savesystem of algebraic operations defined for remainders under division by a fixed positive integer; system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus
AI overview
Modular arithmetic is a system where numbers wrap around when they reach a certain fixed value, called the modulus, so you only work with the remainders left after division. It's useful because it simplifies problems involving cycles and patterns, such as telling time on a clock or organizing data in computer science.
AI-generated from the Wikipedia summary — may contain errors.
Article
Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12.
In mathematics, modular arithmetic is a system of arithmetic operations for integers, differing from the usual ones in that numbers "wrap around" when reaching or exceeding a certain value, called the modulus. The modern approach to number theory using modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.