• Repdigits as products of two Fibonacci or Lucas numbers

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      https://www.ias.ac.in/article/fulltext/pmsc/130/0028

    • Keywords

       

      Fibonacci number; Lucas number; repdigit; Diophantine equations; linear forms in logarithms

    • Abstract

       

      In this study, we show that if $2 \leq m \leq n$ and $F_{m} F_{n}$ represents a repdigit, then $(m, n)$ belongs to the set $$\{(2, 2), (2, 3), (3, 3), (2, 4), (3, 4), (4, 4), (2, 5), (2, 6), (2, 10)\}.$$ Also, we show that if $0 \leq m \leq n$ and $L_{m} L_{n}$ represents a repdigit, then $(m, n)$ belongs to the set $$\left\{ \begin{array}{l}(0, 0), (0, 1), (1, 1), (0, 2), (1, 2), (2, 2), (0, 3),\\ (1, 3), (1, 4), (1, 5), (2, 5), (3, 5), (4, 5) \end{array}\right\}$$

    • Author Affiliations

       

      FATIH ERDUVAN1 REFIK KESKIN1

      1. Mathematics Department, Sakarya University, Sakarya, Turkey
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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