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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A sharp bound for positive solutions of homogeneous linear Diophantine equations


Author: I. Borosh
Journal: Proc. Amer. Math. Soc. 60 (1976), 19-21
MSC: Primary 15A06
MathSciNet review: 0422300
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0422300-8
PII: S 0002-9939(1976)0422300-8
Article copyright: © Copyright 1976 American Mathematical Society