Repdigits as sums of three balancing numbers

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Let $ \{B_{n}\}_{n\geq 0} $ be the sequence of balancing numbers defined by $ B_0=0 $, $ B_1 =1$, and $ B_{n+2}= 6B_{n+1} -B_n$ for all $ n\geq 0 $. In this paper, we find all repdigits in base $ 10 $ which can be written as a sum of three balancing numbers.
Original languageEnglish
Pages (from-to)557-566
JournalMathematica Slovaca
Issue number3
Early online date23 May 2020
Publication statusPublished - 1 Jun 2020


  • Balancing number
  • linear form in logarithms
  • reduction method
  • repdigit

ASJC Scopus subject areas

  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

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