Skip to main content
Log in

Balancing numbers which are concatenation of two repdigits

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

Abstract

In this paper, we show that 35 is the only balancing number which is concatenation of two repdigits.

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

Access this article

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. Alahmadi, A., Altassan, A., Luca, F., Shoaib, H.: Fibonacci numbers which are concatenations of two repdigits. Quaest. Math. (2019). https://doi.org/10.2989/16073606.2019.1686439

    Article  Google Scholar 

  2. Behera, A., Panda, G.K.: On the square roots of triangular numbers. Fib. Quart. 37(2), 98–105 (1999)

    MathSciNet  MATH  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(3), 969–1018 (2006)

    Article  MathSciNet  Google Scholar 

  4. Dujella, A., Pethö, A.: A generalization of a theorem of Baker and Davenport. Quart. J. Math. Oxford Ser. 49(2), 291–306 (1998)

    Article  MathSciNet  Google Scholar 

  5. 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 

  6. Irmak, N., Togbé, A.: On repdigits as product of consecutive Lucas numbers. Notes Numb. Theory Disc. Math. 24(3), 95–102 (2018)

    Article  Google Scholar 

  7. Keskin, R., Erduvan, F.: Repdigits in the base \(b\) as sum of four balancing numbers. Math. Bohemica (2020). https://doi.org/10.21136/MB.2020.0077-19

    Article  MATH  Google Scholar 

  8. Luca, F.: Fibonacci and Lucas numbers with only one distinct digit. Port. Math. 57(2), 243–254 (2000)

    MathSciNet  MATH  Google Scholar 

  9. 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 

  10. 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, 1217–1269 (2000))

    Article  MathSciNet  Google Scholar 

  11. Panda, G.K.: Some fascinating properties of balancing numbers. In: Proceeding of the Eleventh International Conference on Fibonacci Numbers and Their Applications, vol. 194. Congressus Numerantium, 2005. pp. 185–189 (2009)

  12. Ray, P.K.: Balancing and cobalancing numbers. National Institute of Technology, Rourkela (2009). Ph.D. Thesis

  13. Rayaguru, S.G., Panda, G.K.: Repdigits as product of consecutive balancing and Lucas-balancing numbers. Fibonacci Quart. 56(4), 319–324 (2018)

    MathSciNet  MATH  Google Scholar 

  14. Rayaguru, S.G., Panda, G.K.: Repdigits as product of balancing and Lucas-balancing numbers with indices in arithmetic progressions. Fibonacci Quart. 57(3), 231–237 (2019)

    MathSciNet  MATH  Google Scholar 

  15. Waldshmidt, M.: Diophantine approximation on linear algebraic groups: transcendence properties of the exponential function in several variables. Springer, Berlin (2000)

    Book  Google Scholar 

Download references

Acknowledgements

The authors want to express their sincere gratitude to the anonymous referee for his valuable comments and suggestions which improved the presentation of the paper to a great extent.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sai Gopal Rayaguru.

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

Rayaguru, S.G., Panda, G.K. Balancing numbers which are concatenation of two repdigits. Bol. Soc. Mat. Mex. 26, 911–919 (2020). https://doi.org/10.1007/s40590-020-00293-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40590-020-00293-0

Keywords

Mathematics Subject Classification

Navigation