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 language | English |
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Pages (from-to) | 314-321 |
Number of pages | 8 |
Journal | Indagationes Mathematicae |
Volume | 33 |
Issue number | 2 |
DOIs | |
Publication status | Published - Mar 2022 |
Keywords
- Diophantine equations
- Lucas sequences
ASJC Scopus subject areas
- Mathematics(all)