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Perfect powers in elliptic divisibility sequences

Perfect powers in elliptic divisibility sequences
椭圆整除序列的完美幂
批准号:
2604766
负责人:
金额:
$0.0万
依托单位:
依托单位国家:
英国
项目类别:
Studentship
财政年份:
2021
资助国家:
英国
项目状态:
未结题
起止时间:
2021 至 --

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英文摘要
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.
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