Skip to main content
SpringerLink
Log in

Pell and Pell–Lucas Numbers as Sums of Two Repdigits

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

In this paper, we find all Pell and Pell–Lucas numbers expressible as sums of two base 10 repdigits.

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.

Similar content being viewed by others

References

  1. Alvarado, S.D., Luca, F.: Fibonacci numbers which are sums of two repdigits. Proceedings of the XIVth International Conference on Fibonacci numbers and their applications, Sociedad Matematica Mexicana, Aportaciones Matemáticas, Investigación, vol. 20, pp. 97–108 (2011)

  2. Bravo, J.J., Luca, F.: On a conjecture about repdigits in k-generalized Fibonacci sequences. Publ. Math. Debr. 82, 623–639 (2013)

    Article  MathSciNet  Google Scholar 

  3. Bugeaud, Y., Maurice, M., Siksek, S.: Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers. Ann. Math. 163, 969–1018 (2006)

    Article  MathSciNet  Google Scholar 

  4. Bugeaud, Y., Mignotte, M.: On integers with identical digits. Mathematika 46, 411–417 (1999)

    Article  MathSciNet  Google Scholar 

  5. Carmichael, R.D.: On the numerical factors of the arithmetic forms \(\alpha ^n\pm \beta ^n\). Ann. Math. (2) 15, 30–70 (1913)

    Article  MathSciNet  Google Scholar 

  6. de Weger, B.M.M.: Algorithms for diophantine equations. Stichting Mathematisch Centrum, Amsterdam (1989)

  7. Dossavi-Yovo, A., Luca, F., Togbé, A.: On the \(x\)-coordinates of Pell equations which are rep-digits. Publ. Math. Debr. 88, 3–4 (2016)

  8. Faye, B., Luca, F.: Pell and Pell–Lucas numbers with only one distinct digit. Ann. Math. Inform. 45, 55–60 (2015)

    MathSciNet  MATH  Google Scholar 

  9. Luca, F.: Fibonacci and Lucas numbers with only one distinct digit. Port. Math. 57, 243–254 (2000)

    MathSciNet  MATH  Google Scholar 

  10. Luca, F.: Distinct digits in base b expansions of linear recurrence sequences. Quaest. Math. 23, 389–404 (2000)

    Article  MathSciNet  Google Scholar 

  11. Luca, F.: Repdigits which are sums of at most three Fibonacci number. Math. Comm. 17, 1–11 (2012)

    Google Scholar 

  12. Marques, D., Togbé, A.: On terms of linear recurrence sequences with only one distinct block of digits. Colloq. Math. 124, 145–155 (2011)

    Article  MathSciNet  Google Scholar 

  13. Marques, D., Togbé, A.: On repdigits as product of consecutive Fibonacci numbers. Rend. Istit. Mat. Univ. Trieste 44, 393–397 (2012)

    MathSciNet  MATH  Google Scholar 

  14. Matveev, E.M.: An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II. Izv. Ross. Akad. Nauk Ser. Mat. 64, 125–180 (2000). English translation in Izv. Math. 64 (2000), 1217–1269

Download references

Author information

Authors and Affiliations

  1. Institut de Mathématiques et de Sciences Physiques, Dangbo, Bénin

    Chèfiath Adegbindin

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

    Florian Luca

  3. Department of Mathematics, Statistics and Computer Science, Purdue University Northwest, 1401 S, U.S. 421, Westville, IN, 46391, USA

    Alain Togbé

Authors
  1. Chèfiath Adegbindin
    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

  3. Alain Togbé
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alain Togbé.

Additional information

Communicated by Emrah Kilic.

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

Adegbindin, C., Luca, F. & Togbé, A. Pell and Pell–Lucas Numbers as Sums of Two Repdigits. Bull. Malays. Math. Sci. Soc. 43, 1253–1271 (2020). https://doi.org/10.1007/s40840-019-00739-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40840-019-00739-3

Keywords

Mathematics Subject Classification

Search

Navigation