Modular arithmetic

This article is about the concept that uses the "a (mod m)" notation. For the binary operation mod(a,m), see Modulo.

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.

Modular arithmetic modulo m consists of systematically replacing the results of additions, multiplications, and subtractions by the remainder of the division by m. A remarkable property of modular arithmetic is that the result of a computation does not depend on whether the division by m is performed after each operation, only once at the end of the computation, or at the end of the computation and after some intermediate results—typically when an intermediate result becomes too large.

This article is issued from Wikipedia. The text is available under Creative Commons Attribution-Share Alike 4.0 unless otherwise noted. Additional terms may apply for the media files.