Skip to main content
SpringerLink
Log in

Fibonacci numbers which are products of three Pell numbers and Pell numbers which are products of three Fibonacci numbers

  • Original Article
  • Published:
Boletín de la Sociedad Matemática Mexicana Aims and scope Submit manuscript

Abstract

In this paper, we find all the Fibonacci numbers which are products of three Pell numbers and all Pell numbers which are products of three Fibonacci 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. Alekseyev, M.A.: On the intersections of Fibonacci, Pell, and Lucas numbers. Integers 11, 239–259 (2011)

    Article  MathSciNet  Google Scholar 

  2. Ddamulira, M., Luca, F., Rakotomalala, M.: Fibonacci numbers which are products of two Pell numbers. Fibonacci Q. 54(1), 11–18 (2016)

    MathSciNet  MATH  Google Scholar 

  3. Dujella, A., Pethő, A.: A generalization of a theorem of baker and davenport. Q. J. Math. Oxf. Ser. (2) 49(195), 291–306 (1998)

    Article  MathSciNet  Google Scholar 

  4. Matveev, E.M.: An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II. Izv. Math. 64(6), 1217–1269 (2000)

    Article  MathSciNet  Google Scholar 

  5. Weger, B.M.M.: Algorithms for Diophantine Equations. Stichting Mathematisch Centrum, Amsterdam (1989)

    MATH  Google Scholar 

Download references

Acknowledgements

We thank the referee for comments which improved the quality of this manuscript. SER and YA were partially supported by DGRSDT. This paper was completed when the first and the second authors were visiting the third author at the Mohamed First university. They thank the university for the warm welcome and the support.

Author information

Authors and Affiliations

  1. Laboratory of Algebra and Number Theory, Faculty of Mathematics, University of Sciences and Technology Houari Boumediene, BP 32, 16111, Algiers, Algeria

    Salah Eddine Rihane

  2. Department of Mathematics and Computer Sciences, University Center of Mila, BP 26, 43000, Mila, Algeria

    Salah Eddine Rihane

  3. Department of Mathematics and Computer Sciences, École Normale Supérieur, Constantine, Algiers, Algeria

    Youssouf Akrour

  4. LMAM laboratory, Mohamed Seddik Ben Yahia University, Jijel, Algeria

    Youssouf Akrour

  5. ACSA Laboratory, Department of mathematics, Faculty of Sciences, Mohamed First university, Oujda, Morocco

    Abdelaziz El Habibi

Authors
  1. Salah Eddine Rihane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Youssouf Akrour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abdelaziz El Habibi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Salah Eddine Rihane.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rihane, S.E., Akrour, Y. & El Habibi, A. Fibonacci numbers which are products of three Pell numbers and Pell numbers which are products of three Fibonacci numbers. Bol. Soc. Mat. Mex. 26, 895–910 (2020). https://doi.org/10.1007/s40590-020-00296-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40590-020-00296-x

Keywords

Mathematics Subject Classification

Search

Navigation