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
DOI:
https://doi.org/10.1090/S0002-9939-1976-0422300-8
MathSciNet review:
0422300
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- 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 https://doi.org/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, Academic Press, New York-London, 1972. Pure and Applied Mathematics, Vol. 45. MR 0340283
- Serge Lang, Introduction to transcendental numbers, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0214547
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A06
Retrieve articles in all journals with MSC: 15A06
Additional Information
Article copyright:
© Copyright 1976
American Mathematical Society
