关于椭圆可整除序列的完全幂的有限性

IF 0.3 4区数学 Q4 MATHEMATICS Journal De Theorie Des Nombres De Bordeaux Pub Date : 2021-12-17 DOI:10.5802/jtnb.1244

Abdulmuhsin Alfaraj

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引用次数: 1

摘要

我们证明了由$y^2＝x（x^2+b）$的椭圆曲线上的非积分点生成的椭圆可分序列中存在有限多个完全幂，其中$b$是任何正整数。我们通过使用实二次数域上椭圆曲线的模块性来实现这一点。

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On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences

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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