On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences

Abdulmuhsin Alfaraj

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arXiv · 2112.09758

On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences

Abdulmuhsin Alfaraj

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Abstract

We prove that there are finitely many perfect powers in elliptic divisibility sequences generated by a non-integral point on elliptic curves of the from $y^2=x(x^2+b)$, where $b$ is any positive integer. We achieve this by using the modularity of elliptic curves over real quadratic number fields.

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Abdulmuhsin Alfaraj. 2021-12-17. On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences. https://arxiv.org/abs/2112.09758

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