关于丢番图方程 $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$

Pagdame Tiebekabe; Ismaïla Diouf

关于丢番图方程 $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$

数论 2022-09-27 v2

作者: Pagdame Tiebekabe , Ismaïla Diouf

摘要

设 $(F_n)_{n\geq 0}$ 为由 $F_0 = 0, F_1 = 1$ 及 $n \geq 0$ 时 $F_{n+2} = F_{n+1}+F_n$ 给出的斐波那契数列。本文中,我们确定了所有可表示为五个斐波那契数之和的 2 的幂,仅有少量我们已刻画的例外。我们还提出了一个与本文所研究此类方程的解的个数相关的开放问题。

关键词

丢番图方程斐波那契数 2 的幂开放问题

引用

@article{arxiv.2209.07871,
  title  = {On the Diophantine equation $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$},
  author = {Pagdame Tiebekabe and Ismaïla Diouf},
  journal= {arXiv preprint arXiv:2209.07871},
  year   = {2022}
}

备注

This article was presented at the 20th International Conference on Fibonacci Numbers and their Applications in Bosnia at the University of Sarajevo. arXiv admin note: substantial text overlap with arXiv:2202.10127

关于丢番图方程 $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$

摘要

关键词

引用

备注

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