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arXiv · 1511.01970

On a divisibility relation for Lucas sequences

Yuri Bilu·Takao Komatsu·Florian Luca·Amalia Pizarro-Madariaga·Pantelimon Stanica
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Abstract

In this note, we study the divisibility relation $U_m\mid U_{n+k}^s-U_n^s$, where ${\bf U}:=\{U_n\}_{n\ge 0}$ is the Lucas sequence of characteristic polynomial $x^2-ax\pm 1$ and $k,m,n,s$ are positive integers.

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Yuri Bilu, Takao Komatsu, Florian Luca, Amalia Pizarro-Madariaga, Pantelimon Stanica. 2015-11-24. On a divisibility relation for Lucas sequences. https://arxiv.org/abs/1511.01970

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