English

Zeckendorf representations with at most two terms to x-coordinates of Pell equations

Number Theory 2018-03-29 v1

Abstract

In this paper, we find all positive squarefree integers d such that the Pell equation X2-dY2 = +-1 has at least two positive integer solutions (X,Y) and (X',Y') such that both X and X' have Zeckendorf representations with at most two terms. This paper has been accepted for publication in SCIENCE CHINA Mathematics.

Keywords

Cite

@article{arxiv.1803.10732,
  title  = {Zeckendorf representations with at most two terms to x-coordinates of Pell equations},
  author = {Carlos Alexis Gómez and Florian Luca},
  journal= {arXiv preprint arXiv:1803.10732},
  year   = {2018}
}