The Frobenius number associated with the number of representations for sequences of repunits
The generalized Frobenius number is the largest integer represented in at most $p$ ways by a linear combination of nonnegative integers of given positive integers $a_1,a_2,\,\dots ,\,a_k$. When $p=0$, it reduces to the classical Frobenius number. In this paper, we give the generalized Frobenius numb...
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.394/ |
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| author | Komatsu, Takao |
| author_facet | Komatsu, Takao |
| author_sort | Komatsu, Takao |
| collection | DOAJ |
| description | The generalized Frobenius number is the largest integer represented in at most $p$ ways by a linear combination of nonnegative integers of given positive integers $a_1,a_2,\,\dots ,\,a_k$. When $p=0$, it reduces to the classical Frobenius number. In this paper, we give the generalized Frobenius number when $a_j=(b^{n+j-1}-1)/ (b-1)$ ($b\ge 2$) as a generalization of the result of $p=0$ in [16]. |
| format | Article |
| id | doaj-art-08a26b3034494690b03c1bf80ca6f1fd |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-08a26b3034494690b03c1bf80ca6f1fd2025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G1738910.5802/crmath.39410.5802/crmath.394The Frobenius number associated with the number of representations for sequences of repunitsKomatsu, Takao0Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018 ChinaThe generalized Frobenius number is the largest integer represented in at most $p$ ways by a linear combination of nonnegative integers of given positive integers $a_1,a_2,\,\dots ,\,a_k$. When $p=0$, it reduces to the classical Frobenius number. In this paper, we give the generalized Frobenius number when $a_j=(b^{n+j-1}-1)/ (b-1)$ ($b\ge 2$) as a generalization of the result of $p=0$ in [16].https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.394/ |
| spellingShingle | Komatsu, Takao The Frobenius number associated with the number of representations for sequences of repunits Comptes Rendus. Mathématique |
| title | The Frobenius number associated with the number of representations for sequences of repunits |
| title_full | The Frobenius number associated with the number of representations for sequences of repunits |
| title_fullStr | The Frobenius number associated with the number of representations for sequences of repunits |
| title_full_unstemmed | The Frobenius number associated with the number of representations for sequences of repunits |
| title_short | The Frobenius number associated with the number of representations for sequences of repunits |
| title_sort | frobenius number associated with the number of representations for sequences of repunits |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.394/ |
| work_keys_str_mv | AT komatsutakao thefrobeniusnumberassociatedwiththenumberofrepresentationsforsequencesofrepunits AT komatsutakao frobeniusnumberassociatedwiththenumberofrepresentationsforsequencesofrepunits |