A Multivariable Chinese Remainder Theorem
History and Overview
2012-06-25 v1 Number Theory
Abstract
Using an adaptation of Qin Jiushao's method from the 13th century, it is possible to prove that a system of linear modular equations a(i,1) x(i) + ... + a(i,n) x(n) = b(i) mod m(i), i=1, ..., n has integer solutions if m(i)>1 are pairwise relatively prime and in each row, at least one matrix element a(i,j) is relatively prime to m(i). The Chinese remainder theorem is the special case, where A has only one column.
Cite
@article{arxiv.1206.5114,
title = {A Multivariable Chinese Remainder Theorem},
author = {Oliver Knill},
journal= {arXiv preprint arXiv:1206.5114},
year = {2012}
}
Comments
16 pages, 1 figure, (this is an update from a January 2005 paper)