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}
}
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10 pages