modular arithmetic
in its most elementary form, arithmetic done with a count that resets itself to zero every time a certain whole number N greater than one, known as the modulus (mod), has been reached. Examples are a digital clock in the 24-hour system, which resets itself to 0 at midnight (N = 24), and a circular protractor marked in 360 degrees (N = 360). Modular arithmetic is important in number theory, where it is a fundamental tool in the solution of Diophantine equations (particularly those restricted to integer solutions). Generalizations of the subject led to important 19th-century attempts to prove Fermat's last theorem and the development of significant parts of modern algebra.
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