Let m1, m2,…, mk be integers, no two of which have a common factor greater than one. Given a large positive integer n it is possible to compute the remainders or residues r1, r2,…, rk such that n ≡ r1 (mod m1) n ≡ r2 (mod m2) … n ≡ rk (mod mk)
Provided n is less than m1 × m2 × … × mk
n can be represented by (r1,r2,…,rk)
This can be regarded as an internal representation of n. Addition, subtraction, and multiplication of two large numbers then involves the addition, subtraction, and multiplication of corresponding pairs, e.g. (r1,…,rk) + (s1,…,sk) = (r1 + s1, …, rk + sk)
Determining the sign of an integer or comparing relative magnitudes are less straightforward.
"modular arithmetic." A Dictionary of Computing. . Encyclopedia.com. (April 20, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/modular-arithmetic
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