A Multivariable Chinese Remainder Theorem [article]

Oliver Knill
2012 arXiv   pre-print
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.
arXiv:1206.5114v1 fatcat:ubrhu7egx5g3jh3d3hqwpo72m4