Distinct Lengths Modular Zero-sum Subsequences: A Proof of Graham's Conjecture
| dc.creator | Gao, Weidong | |
| dc.creator | Hamidoune, Y. O. | |
| dc.creator | Wang, Guoqing | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:47:32Z | |
| dc.date.available | 2026-07-07T12:47:32Z | |
| dc.description | Let $n$ be a positive integer and let $S$ be a sequence of $n$ integers in the interval $[0,n-1]$. If there is an $r$ such that any nonempty subsequence with sum $\equiv 0$ $\pmod n$ has length $=r,$ then $S$ has at most two distinct values. This proves a conjecture of R. L. Graham. A previous result of P. Erdős and E. Szemerédi shows the validity of this conjecture if $n$ is a large prime number. | |
| dc.identifier | https://arxiv.org/abs/0902.4758 | |
| dc.identifier | http://arxiv.org/abs/0902.4758 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221754 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B60, 11B34; 20D60; 05E15 | |
| dc.title | Distinct Lengths Modular Zero-sum Subsequences: A Proof of Graham's Conjecture | |
| dc.type | text |