On solutions of the Diophantine equation F_{n_{۱}}+F_{n_{۲}}+F_{n_{۳}}+F_{n_{۴}}=۲^a

Let (F_n)_{n\geq ۰} be the Fibonacci sequence given by F_۰ = ۰, F_۱ = ۱ and F_{n+۲} = F_{n+۱}+F_n for n \geq ۰. In this paper, we solve all powers of two which are sums of four Fibonacci numbers with a few exceptions that we characterize.

کلیدواژه ها:

Linear forms in logarithm ، Diophantine equations ، Fibonacci sequence ، Lucas sequence ، perfect powers