扭曲费马三次体的完美幂
Perfect powers generated by the twisted Fermat cubic
摘要：
在扭曲的费马三次函数上，一个椭圆整除序列作为单个有理点的倍数的乘子序列而出现。证明了首项大于1的序列中存在n个完全幂。此外，如果第一项可被6整除，并且生成点是另一个有理点的三倍，则序列中不存在完全幂，除了可能在首项中存在某个l整除2阶的l的l次幂。
英文摘要：
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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