Skip to main content
Log in

On divisibility properties of integers of the form ab + 1

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

Abstract

We give estimates for the cardinality of the sets A , B ⊆ {1, 2,...,N} with the property that ab + 1 is squarefree for all a ∈ A, b ∈ B .

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. P. ErdŐs and A. SÁrkÖzy, On divisibility properties of integers of the form a + a′, Acta Math. Hungar. 50 (1987), 117–122.

    Google Scholar 

  2. P. ErdŐs and P. TurÁn, On a problem in the elementary theory of numbers, American Math. Monthly 41 (1934), 608–611.

    Google Scholar 

  3. K. GyŐry, C. L. Stewart and R. Tijdeman, On prime factors of sums of integers, I, Compositio Math. 59 (1986), 81–88.

    Google Scholar 

  4. J. C. Lagarias, A. M. Odlyzko and J. B. Shearer, On the density of sequences of integers the sum of no two of which is a square, I and II, J. Comb. Theory 33 (1982), 167–185 and 34 (1983), 123–139.

    Google Scholar 

  5. L. LovÁsz, Combinatorical Problems and Exercises, Akadémiai Kiadó, Budapest, 1979.

    Google Scholar 

  6. A. SÁrkÖzy, Unsolved problems in number theory, Periodica Math. Hungar., this volume.

  7. G. N. SÁrkÖzy, On a problem of Erdős, Acta Math. Hungar. 60 (1992), 271–282.

    Google Scholar 

  8. P. TurÁn, On the theory of graphs, Coll. Math. 3 (1953) 19–30.

    Google Scholar 

  9. S. Wigert, Sur l'ordre de grandeur du nombre de diviseurs d'un entier, Arkiv för Mathematik 3 (1906/1907), 1–9.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gyarmati, K. On divisibility properties of integers of the form ab + 1. Periodica Mathematica Hungarica 43, 71–79 (2002). https://doi.org/10.1023/A:1015229531017

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015229531017

Keywords

Navigation