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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Bounds on positive integral solutions of linear Diophantine equations

Authors: I. Borosh and L. B. Treybig
Journal: Proc. Amer. Math. Soc. 55 (1976), 299-304
MathSciNet review: 0396605
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Abstract: Assuming the existence of a solution, we find bounds for small solutions $ x$ of the finite matrix equation $ Ax = B$, where each entry of $ A,B$ is an integer, and $ x$ is a nontrivial column vector with nonnegative integer entries.

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Keywords: Linear equations, integer entries, nonnegative integral solution, bounds, polyhedral convex cones, minors, adjoint matrix
Article copyright: © Copyright 1976 American Mathematical Society