An extension of the Frobenius coin-exchange problem
| dc.creator | Beck, Matthias | |
| dc.creator | Robins, Sinai | |
| dc.date | 2002-04-02 | |
| dc.date.accessioned | 2026-07-07T06:24:26Z | |
| dc.date.available | 2026-07-07T06:24:26Z | |
| dc.description | Given positive integers $a_1,...,a_n$ with $\gcd(a_1,...,a_n) = 1$, we call an integer t representable if there exist nonnegative integers $m_1,...,m_n$ such that $t = m_1 a_1 + ... + m_n a_n$. In this paper, we discuss the linear diophantine problem of Frobenius: namely, find the largest integer which is not representable. We call this largest integer the Frobenius number $g(a_1,...,a_n)$. We extend this problem to asking for the smallest integer $g_k(a_1,...,a_d)$ beyond which every integer is represented more than k times. We concentrate on the case d=2 and prove statements about $g_k(a,b)$ similar in spirit to classical results known about g(a,b). | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0204037 | |
| dc.identifier | http://arxiv.org/abs/math/0204037 | |
| dc.identifier | Number Theory. New York Seminar 2003 (D. Chudnovsky, G. Chudnovsky, M. Nathanson, eds.), 2004, Springer, 17-23. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96540 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11D04, 05A15, 11H06 | |
| dc.title | An extension of the Frobenius coin-exchange problem | |
| dc.type | text |