Sums of Fibonacci numbers close to a power of 2

Abstract

In this paper, we find all sums of two Fibonacci numbers which are close to a power of 2. As a corollary, we also determine all Lucas numbers close to a power of 2. The main tools used in this work are lower bounds for linear forms in logarithms due to Matveev and Dujella–Pethö version of the Baker–Davenport reduction method in diophantine approximation. This paper continues and extends the previous work of Chern and Cui.