Bounds for solution of linear diophantine equations
Optimization and Control
2008-07-01 v1 Number Theory
Abstract
Given linear diophantine equation Ax=b, rank A=m. Let d be the maximum of absolute values of the mxm minors of the matrix (A | b). It is shown that if M={x : Ax=b, x nonnegative and integer} is nonempty, then there exists x=(x1,...,xn) in M, such that xi does not exceed d (i=1,2,..,n).
Keywords
Cite
@article{arxiv.0806.4966,
title = {Bounds for solution of linear diophantine equations},
author = {S. I. Veselov},
journal= {arXiv preprint arXiv:0806.4966},
year = {2008}
}