# Chinese remainder theorem

(algorithm)

Definition: An integer n can be solved uniquely mod LCM(A(i)), given modulii (n mod A(i)), A(i) > 0 for i=1..k, k > 0. In other words, given the remainders an integer gets when it's divided by an arbitrary set of divisors, you can uniquely determine the integer's remainder when it is divided by the least common multiple of those divisors.

Note: For example, knowing the remainder of n when it's divided by 3 and the remainder when it's divided by 5 allows you to determine the remainder of n when it's divided by LCM(3,5) = 15. After LK.

Author: PEB

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

Entry modified 17 December 2004.
HTML page formatted Fri Mar 25 16:20:34 2011.

Cite this as:
Paul E. Black, "Chinese remainder theorem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 17 December 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/chineseRmndr.html