Distinct Lengths Modular Zero-sum Subsequences: A Proof of Graham's Conjecture

dc.creatorGao, Weidong
dc.creatorHamidoune, Y. O.
dc.creatorWang, Guoqing
dc.date2009-02-27
dc.date.accessioned2026-07-07T12:47:32Z
dc.date.available2026-07-07T12:47:32Z
dc.descriptionLet $n$ 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.identifierhttps://arxiv.org/abs/0902.4758
dc.identifierhttp://arxiv.org/abs/0902.4758
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221754
dc.subjectNumber Theory
dc.subjectCombinatorics
dc.subject11B60, 11B34; 20D60; 05E15
dc.titleDistinct Lengths Modular Zero-sum Subsequences: A Proof of Graham's Conjecture
dc.typetext

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