Multiplicative Diophantine equations with factors from different Lucas sequences

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• 作者：Carlos Alexis Gó ; mez Ruiz^a ; ^{carlos.a.gomez@correounivalle.edu.co" class="auth_mail" title="E-mail the corresponding author} ; Florian Luca^b ; ^c ; ^{florian.luca@wits.ac.za" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11B39 ; 11D61 ; 11J86
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：170
• 期：Complete
• 页码：282-301
• 全文大小：386 K

文摘

Let k≥2$k\ge 2$ and ${\{u_n^{(1)}\}}_{n\ge 0},\dots ,{\{u_n^{(k)}\}}_{n\ge 0}$ be k different nondegenerate binary recurrent sequences of integers. In this paper, we show that under certain conditions, there are only finitely many of k  -tuples of the form $(u_{n_1}^{(1)},\dots ,u_{n_k}^{(k)})$ whose contents are multiplicatively dependent. Furthermore, we determine all such instances when k=3$k=3$ and the three sequences are the sequence of Fibonacci numbers, Pell numbers, and base 10 repunits, respectively.