On sums of Fibonacci numbers with few binary digits
Ingrid Vukusic, Volker Ziegler · Publicationes Mathematicae Debrecen · 2021
In this paper we completely solve the Diophantine equation Fn+ Fm = 2 a 1 + 2 a 2 + 2 a 3 + 2 a 4 + 2 a 5 , where F k denotes the k-th Fibonacci number.In addition to complex linear forms in logarithms and the Baker-Davenport reduction method, we use p-adic versions of both tools.