Chinese remainder theorem
Sign in to saveAlso known as CRT, Sunzi theorem
theorem for solving simultaneous congruences
In the Vinony graph
Within Vinony's link graph, Chinese remainder theorem is referenced by 165 other articles, and connects out to time complexity, coprime and modular arithmetic.
It is catalogued under topics including Chinese mathematical discoveries, Commutative algebra and Modular arithmetic.
Its subject is documented across 42 Wikipedia language editions.
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Encyclopedic overview
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1).
Sunzi's original formulation: x ≡ 2 (mod 3) ≡ 3 (mod 5) ≡ 2 (mod 7) with the solution x = 23 + 105k, with k an integer The theorem is sometimes called Sunzi's theorem. Both names of the theorem refer to its earliest known statement that appeared in Sunzi Suanjing, a Chinese manuscript written during the 3rd to 5th century CE. This first statement was restricted to the following example:
Excerpted from Wikipedia’s “Chinese remainder theorem” article, available under the CC BY-SA 4.0 licence.