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.References
- I. Borosh and L. B. Treybig, Bounds on positive integral solutions of linear Diophantine equations, Proc. Amer. Math. Soc. 55 (1976), no. 2, 299–304. MR 396605, DOI 10.1090/S0002-9939-1976-0396605-3
- J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708
- Morris Newman, Integral matrices, Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. MR 0340283
- Serge Lang, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0214547
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