Skip to main content
SpringerLink
Log in

Pell numbers with the Lehmer property

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In this paper, we prove that there is no number with the Lehmer property in the sequence of Pell numbers.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Banks, W.D., Luca, F.: Composite integers n for which \(\phi (n)\mid n-1\). Acta Math. Sin. 23, 1915–1918 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Burcsi, P., Czirbusz, S., Farkas, G.: Computational investigation of Lehmer totient problem. Ann. Univ. Sci. Budapest. Sect. Comp. 35, 43–49 (2011)

  3. Cohen, G.L., Hagis, P.: On the number of prime factors of \(n\) if \(\phi (n)\mid n-1\). Nieuw Arch. Wisk. 28(3), 177–185 (1980)

  4. Faye, B., Luca, F.: Lucas numbers with the Lehmer property. Preprint (2015)

  5. Grau Ribas, J.M., Luca, F.: Cullen numbers with the Lehmer property. Proc. Am. Math. Soc. 140, 129–134 (2012); Corrigendum, idem, 141, 2941–2943 (2013)

  6. Kim, D.-J., Oh, B.-K.: Generalized Cullen numbers with the Lehmer property. Bull. Korean Math. Soc. 50, 1981–1988 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lehmer, D.H.: On Euler totient function. Bull. Am. Math. Soc. 38, 745–751 (1932)

  8. Luca, F.: Fibonacci numbers with the Lehmer property. Bull. Pol. Acad. Sci. Math. 55, 7–15 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pomerance, C.: On composite \(n\) for which \(\phi (n)\mid n-1\), II. Pacific J. Math. 69, 177–186 (1977)

    Article  MathSciNet  Google Scholar 

  10. Renze, J.: Computational evidence for Lehmer’s totient conjecture. Published electronically at http://library.wolfram.com/infocenter/MathSource/5483/ (2004)

Download references

Acknowledgments

The authors thank the referee for useful comments. B. F. thanks OWSD and Sida (Swedish International Development Cooperation Agency) for a scholarship during her Ph.D. studies at Wits.

Author information

Authors and Affiliations

  1. Ecole Doctorale de Mathematiques et d’Informatique, Université Cheikh Anta Diop de Dakar, 5005, Dakar Fann, Senegal

    Bernadette Faye

  2. School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits, Johannesburg, 2050, South Africa

    Bernadette Faye & Florian Luca

Authors
  1. Bernadette Faye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Florian Luca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bernadette Faye.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Faye, B., Luca, F. Pell numbers with the Lehmer property. Afr. Mat. 28, 291–294 (2017). https://doi.org/10.1007/s13370-016-0449-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-016-0449-5

Keywords

Mathematics Subject Classification

Search

Navigation