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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A sharp bound for positive solutions of homogeneous linear Diophantine equations
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by I. Borosh PDF
Proc. Amer. Math. Soc. 60 (1976), 19-21 Request permission

Abstract:

Let A be an $m \times n$ matrix of rank r with integer entries. It is proved that if the system $Ax = 0$ has a nontrivial solution in nonnegative integers, then it has such a solution with entries bounded by the maximum of the absolute values of the $r \times r$ minors of A.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 19-21
  • MSC: Primary 15A06
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0422300-8
  • MathSciNet review: 0422300