Generalized Frobenius Number of Three Variables
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910750945050624 |
|---|---|
| author | Subwattanachai, Kittipong |
| author_facet | Subwattanachai, Kittipong |
| contents | For $ k \geq 2 $, we let $ A = (a_{1}, a_{2}, \ldots, a_{k}) $ be a $k$-tuple of positive integers with $\gcd(a_{1}, a_2, \ldots, a_k) =1$ and, for a non-negative integer $s$, the generalized Frobenius number of $A$, $g(A;s) = g(a_1, a_2, \ldots, a_k;s)$, the largest integer that has at most $s$ representations in terms of $a_1, a_2, \ldots, a_k$ with non-negative integer coefficients. In this article, we give a formula for the generalized Frobenius number of three positive integers $(a_1,a_2,a_3)$ with certain conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09149 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Frobenius Number of Three Variables Subwattanachai, Kittipong Number Theory 11D07 (Primary) 11B34 (Secondary) For $ k \geq 2 $, we let $ A = (a_{1}, a_{2}, \ldots, a_{k}) $ be a $k$-tuple of positive integers with $\gcd(a_{1}, a_2, \ldots, a_k) =1$ and, for a non-negative integer $s$, the generalized Frobenius number of $A$, $g(A;s) = g(a_1, a_2, \ldots, a_k;s)$, the largest integer that has at most $s$ representations in terms of $a_1, a_2, \ldots, a_k$ with non-negative integer coefficients. In this article, we give a formula for the generalized Frobenius number of three positive integers $(a_1,a_2,a_3)$ with certain conditions. |
| title | Generalized Frobenius Number of Three Variables |
| topic | Number Theory 11D07 (Primary) 11B34 (Secondary) |
| url | https://arxiv.org/abs/2309.09149 |