Shifted powers in Lucas-Lehmer sequences
Shifted powers in Lucas-Lehmer sequences
复制标题
Lucas-Lehmer 序列中的权力转移
DOI：
10.1007/s40993-019-0153-2
复制
发表时间：
2019
影响因子：
0.8
通讯作者：
Bennett M
中科院分区：
文献类型：
--
作者：
Bennett M
我们开发了一个通用的框架，通过移动非退化的二次Lucas-Lehmer二进制递归序列由一个固定的整数导出的序列中找到所有完美的权力。通过结合这一设置与边界的线性形式的曲线和结果的基础上的模块化的椭圆曲线定义在完全真实的领域，我们能够回答一个问题的Bugeaud，卢卡，Mittette和第三作者明确找到所有完美的权力的形状whereis第k项在斐波那契序列。
We develop a general framework for finding all perfect powers in sequences derived via shifting non-degenerate quadratic Lucas–Lehmer binary recurrence sequences by a fixed integer. By combining this setup with bounds for linear forms in logarithms and results based upon the modularity of elliptic curves defined over totally real fields, we are able to answer a question of Bugeaud, Luca, Mignotte and the third author by explicitly finding all perfect powers of the shapewhereis thek-th term in the Fibonacci sequence.