A sharp bound for solutions of linear Diophantine equations
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- by I. Borosh, M. Flahive, D. Rubin and B. Treybig PDF
- Proc. Amer. Math. Soc. 105 (1989), 844-846 Request permission
Abstract:
Let $Ax = b$ be an $m \times n$ system of linear equations with rank $m$ and integer coefficients. Denote by $Y$ the maximum of the absolute values of the $m \times m$ minors of the augmented matrix $\left ( {A,b} \right )$. It is proved that if the system has an integral solution, then it has an integral solution $x = \left ( {{x_i}} \right )$ with $\max \left | {{x_i}} \right | \leq Y$. The bound is sharp.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 844-846
- MSC: Primary 15A36; Secondary 11D04, 90C10
- DOI: https://doi.org/10.1090/S0002-9939-1989-0955458-1
- MathSciNet review: 955458