论文标题
在Diophantine方程式上
On the Diophantine equation $\displaystyle \sum _{k=1}^{5}F_{n_k}=2^a$
论文作者
论文摘要
令$（f_n）_ {n \ geq 0} $为$ f_0 = 0给出的fibonacci序列，f_1 = 1 $和$ f_ {n+2} = f_ {n+1}+f_n $ for $ n \ geq 0 $。在本文中，我们确定了2的所有功率，这些功率是五个斐波那契数的总和，我们表征了少数例外。我们还指出了一个与本文研究的方程式数量有关的公开问题。
Let $(F_n)_{n\geq 0}$ be the Fibonacci sequence given by $F_0 = 0, F_1 = 1$ and $F_{n+2} = F_{n+1}+F_n$ for $n \geq 0$. In this paper, we have determined all the powers of 2 which are sums of five Fibonacci numbers with few exceptions that we characterize. We have also stated an open problem relating to the number of solutions of equations like those studied in this paper.
