A bound on solutions of linear integer equalities and inequalities

Authors:
Joachim von zur Gathen and Malte Sieveking

Journal:
Proc. Amer. Math. Soc. **72** (1978), 155-158

MSC:
Primary 52A40; Secondary 15A39, 90C10

DOI:
https://doi.org/10.1090/S0002-9939-1978-0500555-0

MathSciNet review:
0500555

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Abstract: Consider a system of linear equalities and inequalities with integer coefficients. We describe the set of rational solutions by a finite generating set of solution vectors. The entries of these vectors can be bounded by the absolute value of a certain subdeterminant. The smallest integer solution of the system has coefficients not larger than this subdeterminant times the number of indeterminates. Up to the latter factor, the bound is sharp.

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DOI:
https://doi.org/10.1090/S0002-9939-1978-0500555-0

Article copyright:
© Copyright 1978
American Mathematical Society