不具有3AP 整数集的一个新问题

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (1): 145-151.

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A New Problem on Integer Sets Without 3AP

YAO Bing, CHEN Xiang-En

College of Mathematics and Statistics, Northwest Normal University, Lanzhou |730070

Received:2011-03-20 Revised:2012-05-05 Online:2013-02-25 Published:2013-02-25
Supported by:
国家自然科学基金(61163054, 61163037)资助

For each integer k≥3, an anti-average k-set is a set with k nonnegative integers that contains zero and has no three terms in arithmetic progression. We wish to find λ*(k)=min{maxS: S is an anti-average k-set} for every integer k≥3. Some properties and bounds of λ*(k) are shown, and the method of constructing larger anti-average sets are provided.

Key words: Arithmetic progression, Anti-average number, Dual set

CLC Number:

05C78

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YAO Bing, CHEN Xiang-En. A New Problem on Integer Sets Without 3AP[J].Acta mathematica scientia,Series A, 2013, 33(1): 145-151.

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A New Problem on Integer Sets Without 3AP

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