English

Perfect powers generated by the twisted Fermat cubic

Number Theory 2011-02-23 v2

Abstract

On the twisted Fermat cubic, an elliptic divisibility sequence arises as the sequence of denominators of the multiples of a single rational point. It is shown that there are finitely many perfect powers in such a sequence whose first term is greater than 1. Moreover, if the first term is divisible by 6 and the generating point is triple another rational point then there are no perfect powers in the sequence except possibly an lth power for some l dividing the order of 2 in the first term.

Keywords

Cite

@article{arxiv.1102.2793,
  title  = {Perfect powers generated by the twisted Fermat cubic},
  author = {Jonathan Reynolds},
  journal= {arXiv preprint arXiv:1102.2793},
  year   = {2011}
}

Comments

10 pages

R2 v1 2026-06-21T17:25:55.542Z