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Repdigits as Product of Fibonacci and Tribonacci Numbers

Author

Listed:
  • Dušan Bednařík

    (Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic)

  • Eva Trojovská

    (Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic)

Abstract

In this paper, we study the problem of the explicit intersection of two sequences. More specifically, we find all repdigits (i.e., numbers with only one repeated digit in its decimal expansion) which can be written as the product of a Fibonacci by a Tribonacci number (both with the same indexes). To work on this problem, our approach is to combine lower bounds from the Baker’s theory with reduction methods (based on the theory of continued fractions) due to Dujella and Pethö.

Suggested Citation

  • Dušan Bednařík & Eva Trojovská, 2020. "Repdigits as Product of Fibonacci and Tribonacci Numbers," Mathematics, MDPI, vol. 8(10), pages 1-8, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1720-:d:424435
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    References listed on IDEAS

    as
    1. Pavel Trojovský, 2019. "On Terms of Generalized Fibonacci Sequences which are Powers of their Indexes," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
    2. Pavel Trojovský, 2020. "Fibonacci Numbers with a Prescribed Block of Digits," Mathematics, MDPI, vol. 8(4), pages 1-7, April.
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