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On the Linear Diophantine Problem of Frobenius

✍ Scribed by J.L. Davison

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 351 KB
Volume: 48
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1994.1071

No coin nor oath required. For personal study only.

✦ Synopsis

Suppose (a, b, c) are three positive integers with (\mathrm{gcd}=1). We consider the function (f(a, b, c)) defined to be the largest integer not representable as a positive integral linear combination of (a, b, c). We give a new lower bound for (f(a, b, c)) which is shown to be tight, and we give a new proof of a theorem due to Vitek on an upper bound. A polynomial time algorithm, based on modifications to Rodseth and Selmer/Beyer algorithms, is given for the computation of (f(a, b, c)). Finally, some open problems are discussed. C 1994 Academic Press, Inc.

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