English

Markoff-Rosenberger triples and generalized Lucas sequences

Number Theory 2020-05-29 v1

Abstract

We consider the Markoff-Rosenberger equation ax2+by2+cz2=dxyzax^2+by^2+cz^2=dxyz with (x,y,z)=(Ui,Uj,Uk),(x,y,z)=(U_i,U_j,U_k), where UiU_i denotes the ii-th generalized Lucas number of first/second kind. We provide upper bound for the minimum of the indices and we apply the result to completely resolve concrete equations, e.g. we determine solutions containing only balancing numbers and Jacobsthal numbers, respectively.

Cite

@article{arxiv.2005.13935,
  title  = {Markoff-Rosenberger triples and generalized Lucas sequences},
  author = {Hayder Hashim and László Szalay and Szabolcs Tengely},
  journal= {arXiv preprint arXiv:2005.13935},
  year   = {2020}
}
R2 v1 2026-06-23T15:52:53.683Z