Bounds for solution of linear diophantine equations

Details Bounds for solution of linear diophantine equations Bounds for solution of linear diophantine equations

2008-06-30

arxiv.org/abs/0806.4966v1

Mathematics

Optimization and Control

Scientific paper

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).

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