modular arithmetic

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modular arithmetic

(Or "clock arithmetic") A kind of integer arithmetic that reduces all numbers to one of a fixed set [0..N-1] (this would be "modulo N arithmetic") by effectively repeatedly adding or subtracting N (the "modulus") until the result is within this range.

The original mathematical usage considers only __equivalence__ modulo N. The numbers being compared can take any values, what matters is whether they differ by a multiple of N. Computing usage however, considers modulo to be an operator that returns the remainder after integer division of its first argument by its second.

Ordinary "clock arithmetic" is like modular arithmetic except that the range is [1..12] whereas modulo 12 would be [0..11].
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'One simple idea is try to solve equations with modular arithmetic,' he says.
Such advanced algorithms comprise of modular arithmetic, modular exponentiation, prime number theory, Chinese Reminder Theorem, and Fermat's Little Theorem and Euler's Theorem.
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