Perfect powers generated by the twisted Fermat cubic

Details Perfect powers generated by the twisted Fermat cubic Perfect powers generated by the twisted Fermat cubic

2011-02-14

arxiv.org/abs/1102.2793v2

Mathematics

Number Theory

10 pages

Scientific paper

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.

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