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

Kwok Chi Chim; Volker Ziegler

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arXiv · 1705.06468

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

Kwok Chi Chim·Volker Ziegler

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Abstract

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 $\max \{ m_1, m_2, m_3, t_1, t_2 \}\leq 16$.

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BibTeX RIS

Kwok Chi Chim, Volker Ziegler. 2017-05-18. On Diophantine equations involving sums of Fibonacci numbers and powers of $2$. https://arxiv.org/abs/1705.06468

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