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A NOTE ON A RESULT OF RUZSA

Part of: Sequences and sets

Published online by Cambridge University Press:  01 February 2008

MIN TANG
MIN TANG*
Affiliation:
Department of Mathematics, Anhui Normal University, Wuhu 241000, China (email: [email protected])
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Abstract

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Let σA(n)=∣{(a,a′)∈A2:a+a′=n}∣, where and A is a subset of . Erdös and Turán conjectured that, for any basis A of , σA(n) is unbounded. In 1990, Ruzsa constructed a basis for which σA(n) is bounded in the square mean. In this paper, based on Ruzsa’s method, we show that there exists a basis A of satisfying for large enough N.

Keywords

Erdös–Turán conjecturebasis

MSC classification

Secondary: 11B13: Additive bases, including sumsets
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 1 , February 2008 , pp. 91 - 98
Copyright
Copyright © Australian Mathematical Society 2008

References

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