arXiv Analytics

Sign in

arXiv:1705.06468 [math.NT]AbstractReferencesReviewsResources

On Diophantine equations involving sums of Fibonacci numbers and powers of $2$

Kwok Chi Chim, Volker Ziegler

Published 2017-05-18Version 1

In this paper, we completely solve the Diophantine equations $F_{n_1} + F_{n_2} = 2^{a_1} + 2^{a_2} + 2^{a_3}$ and $ F_{m_1} + F_{m_2} + F_{m_3} =2^{t_1} + 2^{t_2} $, where $F_k$ denotes the $k$-th Fibonacci number. In particular, we prove that $\max \{n_1, n_2, a_1, a_2, a_3 \}\leq 18$ and $\max \{ m_1, m_2, m_3, t_1, t_2 \}\leq 16$.

Categories: math.NT
Related articles: Most relevant | Search more
arXiv:2409.02933 [math.NT] (Published 2024-08-21)
A Pair of Diophantine Equations Involving the Fibonacci Numbers
Xuyuan Chen et al.
arXiv:1701.02604 [math.NT] (Published 2017-01-06)
On the Diophantine equations $ \sum_{i=1}^n a_ix_{i} ^6+\sum_{i=1}^m b_iy_{i} ^3= \sum_{i=1}^na_iX_{i}^6\pm\sum_{i=1}^m b_iY_{i} ^3 $
arXiv:2207.03521 [math.NT] (Published 2022-07-07)
On the greatest common divisor of $n$ and the $n$th Fibonacci number, II

Links

Toolbox