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The p-Frobenius Number for the Triple of the Generalized Star Numbers
Version 1
: Received: 26 July 2024 / Approved: 29 July 2024 / Online: 29 July 2024 (09:50:38 CEST)
How to cite: Yin, R.; Mu, J.; Komatsu, T. The p-Frobenius Number for the Triple of the Generalized Star Numbers. Preprints 2024, 2024072280. https://doi.org/10.20944/preprints202407.2280.v1 Yin, R.; Mu, J.; Komatsu, T. The p-Frobenius Number for the Triple of the Generalized Star Numbers. Preprints 2024, 2024072280. https://doi.org/10.20944/preprints202407.2280.v1
Abstract
In this paper, we give closed-form expressions of the $p$-Frobenius number for the triple of the generalized star numbers $a n(n-1)+1$ for an integer $a\ge 4$. When $a=6$, it is reduced to the famous star number. For the set of given positive integers $\{a_1,a_2,\dots,a_k\}$, the $p$-Frobenius number is the largest integer $N$ whose number of nonnegative integer representations $N=a_1 x_1+a_2 x_2+\dots+a_k x_k$ is at most $p$. When $p=0$, the $0$-Frobenius number is the classical Frobenius number, which is the central topic of the famous linear Diophantine problem of Frobenius.
Keywords
frobenius problem; Frobenius numbers; centered 2a-gonal numbers; the number of representations
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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