On a problem of Pillai with Fibonacci numbers and powers of $3$

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Abstract

Consider the sequence $ \{F_{n}\}_{n\geq 0} $ of Fibonacci numbers defined by $ F_0=0 $, $ F_1 =1$ and $ F_{n+2}=F_{n+1}+ F_{n} $ for all $ n\geq 0 $. In this paper, we find all integers $ c $ having at least two representations as a difference between a Fibonacci number and a power of $ 3 $.
Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalBoletín de la Sociedad Matemática Mexicana
DOIs
Publication statusPublished - 17 Sep 2019

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Keywords

  • Fibonacci number
  • Linear forms in logarithms
  • Baker's method

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On a problem of Pillai with Fibonacci numbers and powers of $3$. / Ddamulira, Mahadi.

In: Boletín de la Sociedad Matemática Mexicana, 17.09.2019, p. 1-14.

Research output: Contribution to journalArticleResearchpeer-review

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