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In mathematics, modular arithmetic is special category of arithmetic that makes use of only integers. In other words, modular arithmetic is the arithmetic of congruence. Modular arithmetic is sometimes known as clock arithmetic, as one of the most familiar uses of modular arithmetic is in the 12-hour clock, which has the time period divided into two equal halves.
In his book "Disquistiones Arithmeticae" released in 1801, Carl Friedrich Gauss introduced the modern approach to modular arithmetic. According to mathematics, modular arithmetic is considered as the arithmetic of any non-trivial homomorphic images of the ring of integers. In modular arithmetic, the numerals which are dealt with are only integers and the operations that are used are only addition, subtraction, multiplication and division. In modular arithmetic, the numbers wrap around or round off upon reaching a certain value, making use of modulus. In this form of arithmetic, remainders are considered. Modular arithmetic is usually associated with prime numbers. Two numbers are considered equivalent is the remainders of both numbers divided by a unique number is equal.
For example, if the time is 10:00 and four hours are added, the correct answer is 2:00 rather than 14:00, since the clock wraps around at 12:00.
Modular arithmetic is widely used in date computation, time computation and in discrete computing.