On the problem of Pillai with Tribonacci numbers and powers of 3

Mahadi Ddamulira

Research output: Contribution to journalArticle

Abstract

Let $ (T_{n})_{n\geq 0} $ be the sequence of Tribonacci numbers defined by $ T_0=0 $, $ T_1 = T_2=1$, and $ T_{n+3}=T_{n+2}+ T_{n+1} +T_n$ for all $ n\geq 0 $. In this note, we find all integers $ c $ admitting at least two representations as a difference between a tribonacci number and a power of $ 3 $.
Original languageEnglish
Article number19.5.6
Pages (from-to)1-14
Number of pages14
JournalJournal of Integer Sequences
Volume22
Issue number5
Publication statusPublished - 23 Aug 2019

Keywords

  • Tribonacci sequence
  • Pell equation
  • Linear forms in logarithms
  • Baker's method

ASJC Scopus subject areas

  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

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