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Periodica Mathematica Hungarica

, Volume 15, Issue 3, pp 205–209 | Cite as

Difference sets without squares

  • I. Z. Ruzsa
Article

Abstract

A sequence of natural numbersA=a 1,a 2, ... is constructed such that noa i −a j is a square and there are >x 0,73 a i 's belowx.

AMS (MOS) subject classifications (1970)

Primary 05B10 10L05 

Key words and phrases

Difference sets intersective set 

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References

  1. [1]
    H. Halberstam andK. F. Roth,Sequences, Clarendon, Oxford, 1966.MR 35 # 1565Google Scholar
  2. [2]
    A. Sárközy, On difference sets of sequences of integers, I,Acta Math. Acad. Sci. Hungar. 31 (1978), 125–149.MR 57 # 5942zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    A. Sárközy, On difference sets of sequences of integers, II.Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 21 (1978), 45–53.MR 80j: 10062azbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó 1984

Authors and Affiliations

  • I. Z. Ruzsa
    • 1
  1. 1.MTA Matematikai Kutató IntézetBudapestHungary

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