On the Frobenius Problem

The classical Frobenius problem (the Frobenius coin problem) is considered. Using the method of generating functions, we find an expression for the number of solutions of a Diophantine equation. As a corollary, this result implies the well-known Sylvester–Gallai theorem. In addition, we obtain not o...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics 2022, Vol.16 (2), p.267-275
Main Author: Leontiev, V. K.
Format: Article
Language:English
Subjects:
Cryptography
Diophantine equation
Mathematics
Mathematics and Statistics
Optimization
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Summary:The classical Frobenius problem (the Frobenius coin problem) is considered. Using the method of generating functions, we find an expression for the number of solutions of a Diophantine equation. As a corollary, this result implies the well-known Sylvester–Gallai theorem. In addition, we obtain not only an expression for the Frobenius number, but also formulas for those values of the variables for which this number is attained. The problems in this paper are closely related to discrete optimization problems as well as cryptographic information security methods.
ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478922020089