SMALL SOLUTIONS OF LINEAR DIOPHANTINE EQUATIONS Academic Article

abstract

• Let Ax = B be a system of m n linear equations with integer coefficients. Assume the rows of A are linearly independent and denote by X (respectively Y) the maximum of the absolute values of the m m minors of the matrix A (the augmented matrix (A, B)). If the system has a solution in nonnegative integers, it is proved that the system has a solution X = (xi) in nonnegative integers wity xi X for n - m variables and xi (m - m + 1)Y for m variables. This improves previous results of the authors and others. 1986.

authors

• Borosh, Itshak

published proceedings

• DISCRETE MATHEMATICS

author list (cited authors)

• BOROSH, I., FLAHIVE, M., & TREYBIG, B.

citation count

• 19

complete list of authors

• BOROSH, I||FLAHIVE, M||TREYBIG, B

publication date

• March 1986

publisher

• Elsevier  Publisher

published in

• Discrete Mathematics  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4903 Numerical And Computational Mathematics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1016/0012-365X(86)90138-X

start page

• 215

end page

• 220

volume

• 58

issue

• 3

URL

• http://dx.doi.org/10.1016/0012-365x(86)90138-x