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On the Frobenius Problem

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Abstract

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.

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Funding

This work was supported by the Russian Foundation for Basic Research, project no. 20–01–00645.

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, Russian Academy of Sciences, Moscow, 119333, Russia

    V. K. Leontiev

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  1. V. K. Leontiev
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Correspondence to V. K. Leontiev.

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Translated by V. Potapchouck

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Leontiev, V.K. On the Frobenius Problem. J. Appl. Ind. Math. 16, 267–275 (2022). https://doi.org/10.1134/S1990478922020089

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  • DOI: https://doi.org/10.1134/S1990478922020089

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