Perfect powers in elliptic divisibility sequences

椭圆整除序列的完美幂

• 批准号: 2604766
• 金额: --
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2604766
• 关键词: Perfect; powers; elliptic; divisibility; sequences

The problem of determining all perfect powers in a sequence has always been interesting to mathematicians. The problem we are interested in is to prove that there are finitely many perfect powers in elliptic divisibility sequences. Abdulmuhsin Alfaraj proved 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. The main goal of our project is to generalize this result for elliptic divisibility sequences generated by any non-integral point on all elliptic curves y^2=x^3+ax^2+bx+c.

确定序列中所有完美幂的问题一直是数学家感兴趣的问题。我们感兴趣的问题是证明椭圆整除序列中存在1000个完美幂。Abdulmuhsin Alfaraj证明了由y ^2 =x（x ^2 +B）的椭圆曲线上的一个非整点生成的椭圆整除序列存在n个完美幂，其中B为任意正整数.我们的主要目标是将这个结果推广到所有椭圆曲线y^2=x^3+ax^2+bx+c上的任意非整点生成的椭圆整除序列。