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Sumsets Intersecting a Sequence(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2012年02期
Page:
22-23
Research Field:
数学
Publishing date:

Info

Title:
Sumsets Intersecting a Sequence
Author(s):
Wu Jiandong; Yang Quanhui
School of Mathematical Sciences and Institute of Mathematics,Nanjing Normal University,Nanjing 210046,China
Keywords:
sumsets; sequences
PACS:
O156
DOI:
-
Abstract:
Let { an } ∞ n = 1 be an unbounded sequence of positive integers with an + 1 /an→α as n→∞，and let β ＞ max{ α， 2} ． Then there exists an x0 such that for all x ＞ x0 and if A，B［0，x］ are sets of nonnegative integers with 0∈A∩B and | A| + | B|≥2(1 － 1 ) β x， then the sumset A + B contains an element of the sequence { an } ． This generalizes a recent result by Kapoor V．

References:

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［5］ Pan Hao． Note on integer powers in sumsets［J］． J Number Theory，2006( 117) : 216-221．
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［8］ Nathanson M B． Additive Number Theory: Inverse Problems and the Geometry of Sumsets． Volume 165 of Graduate Texts in Mathematics［M］． New York: Springer-Verlag，1996．
［9］ Kapoor V． Sets whose sumsets avoids a thin sequence［J］． J Number Theory，2010( 130) : 534-538．

Memo

Memo:
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Last Update: 2013-03-11