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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 9, Pages 1447–1457
DOI: https://doi.org/10.31857/S0044466922090046 (Mi zvmmf11445) 		 
This article is cited in 2 scientific papers (total in 2 papers)

General numerical methods

On the number of solutions to linear Diophantine equation and Frobenius problem

E. N. Gordeeva, V. K. Leont'evb

a Bauman Moscow State Technical University, Moscow, Russia
b Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia
Citations (2)
DOI: https://doi.org/10.31857/S0044466922090046
Abstract: Issues concerning the solvability and number of solutions to linear Diophantine equations are considered. Along with the general case, combinatorial characteristics of the number of solutions and the mean number of solutions to equations of a special case are studied. One type of equation represents partitions of a natural number into natural additive components. Another type consists of linear equations in two unknowns that are usually studied in relation to the Frobenius problem. The focus is on three aspects. The first is the solvability and number of solutions of the Diophantine equation when the problem is parameterized with respect to the right-hand side. Formulas and bounds for finding this number both in the general case and in some particular cases are obtained. The second aspect is devoted to the partition problem. The third aspect concerns the Frobenius problem.
Key words: Diophantine equation, partitions, Frobenius problem, Boolean equations, Frobenius number.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00645
This work was supported by the Russian Foundation for Basic Research, project no. 20-01-00645.
Received: 10.09.2021
Revised: 28.02.2022
Accepted: 11.04.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 9, Pages 1413–1423
DOI: https://doi.org/10.1134/S0965542522090044
Bibliographic databases:
Document Type: Article
UDC: 519.16
Language: Russian
Citation: E. N. Gordeev, V. K. Leont'ev, “On the number of solutions to linear Diophantine equation and Frobenius problem”, Zh. Vychisl. Mat. Mat. Fiz., 62:9 (2022), 1447–1457; Comput. Math. Math. Phys., 62:9 (2022), 1413–1423
Citation in format AMSBIB
\Bibitem{GorLeo22}
\by E.~N.~Gordeev, V.~K.~Leont'ev
\paper On the number of solutions to linear Diophantine equation and Frobenius problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 9
\pages 1447--1457
\mathnet{http://mi.mathnet.ru/zvmmf11445}
\crossref{https://doi.org/10.31857/S0044466922090046}
\elib{https://elibrary.ru/item.asp?id=49273352}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 9
\pages 1413--1423
\crossref{https://doi.org/10.1134/S0965542522090044}
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    • This publication is cited in the following 2 articles:
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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