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On the Shorey–Tijdeman Diophantine equation involving terms of Lucas sequences
Journal article   Open access  Peer reviewed

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

Mahadi Ddamulira, Florian Luca and Robert Tichy
Indagationes mathematicae, Vol.33(2), pp.314-321
01/03/2022
DOI: https://doi.org/10.1016/j.indag.2021.08.001

Abstract

Diophantine equations Lucas sequences
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.
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https://doi.org/10.1016/j.indag.2021.08.001View
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