On the Diophantine equation $F_n^2+F_m^2 = 2^a$
- Ga-Hyun Jeong ,
- Poo-Sung Park
Abstract
Let $F_n$ be the $n$-th Fibonacci number. In this paper we show that the only nonnegative solutions $(n,m,a)$ of the Diophantine equation $F_n^2+F_m^2 = 2^a$ with $n \ge m \ge 0$ are $(1,0,0)$, $(2,0,0)$, $(3,0,2)$, $(6,0,6)$, $(1,1,1)$, $(2,1,1)$, $(2,2,1)$, $(3,3,3)$, $(6,6,7)$.Keywords
Fibonacci numbers, Diophantine equation, linear forms in logarithms, reduction method