On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences

Mahadi Ddamulira*, Florian Luca

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Let r≥ 1 be an integer and U:=(Un)n≥0 be the Lucas sequence given by U= 0 , U1= 1 , and Un+2= rUn+1+ Un, for all n≥ 0. In this paper, we show that there are no positive integers r≥3,x≠2,n≥1 such that Unx+Un+1x is a member of U.

Original languageEnglish
Number of pages34
JournalThe Ramanujan Journal
Early online date23 Jul 2020
DOIs
Publication statusE-pub ahead of print - 23 Jul 2020

Keywords

  • Baker’s method
  • Linear forms in logarithms
  • Lucas sequences

ASJC Scopus subject areas

  • Algebra and Number Theory

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