On the Shorey–Tijdeman Diophantine equation involving terms of Lucas sequences

Mahadi Ddamulira*, Florian Luca, Robert Tichy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let r≥1 be an integer and U≔{Un}n≥0 be the Lucas sequence given by U0=0,U1=1, and Un+2=rUn+1+Un for n≥0. In this paper, we explain how to find all the solutions of the Diophantine equation, AUn+BUm=CUn1+DUm1, in integers r≥1, 0≤m<n,0≤m1<n1, AUn≠CUn1, where A,B,C,D are given integers with A≠0,B≠0, m,n,m1,n1 are nonnegative integer unknowns and r is also unknown.

Original languageEnglish
Pages (from-to)314-321
Number of pages8
JournalIndagationes Mathematicae
Volume33
Issue number2
DOIs
Publication statusPublished - Mar 2022

Keywords

  • Diophantine equations
  • Lucas sequences

ASJC Scopus subject areas

  • Mathematics(all)

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