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Multiplicative properties of sets of positive integers

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Abstract

It is proved that every set of positive integers with upper Dirichlet density greater than 1/2 contains three distinct elements whose product is a square. Several similar problems are considered.

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References

  1. E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Reprint Chelsea, 1953.

  2. Ostmann H.: Additive Zahlentheorie. Erster Teil, Springer-Verlag, Berlin (1956)

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  3. P. Turan, An extremal problem in graph theory, Collected papers, Vol. 1, Akadémiai Kiadó, Budapest, 1990, 231–250.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary

    L. Hajdu

  2. Institute of Mathematics, Polish Academy of Sciences, Sniadeckich 8, P.O. Box 21, 00-956, Warszawa, Poland

    A. Schinzel

  3. Institute of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    M. Skałba

Authors
  1. L. Hajdu
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  2. A. Schinzel
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  3. M. Skałba
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Correspondence to M. Skałba.

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Hajdu, L., Schinzel, A. & Skałba, M. Multiplicative properties of sets of positive integers. Arch. Math. 93, 269–276 (2009). https://doi.org/10.1007/s00013-009-0015-6

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  • DOI: https://doi.org/10.1007/s00013-009-0015-6

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