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.

Sums of three Fibonacci numbers close to a power of 2

“…

In this paper, we find all the sums of three Fibonacci numbers which are close to a power of 2. This paper continues and extends the previous work of Hasanalizade [8].

…”

“…in non-negative integer n, k, m with k ≥ 2 and n ≥ 1. Recently, Hasanlizade [8] extended the previous work of [5] by considering the sum of Fibonacci numbers and studied the sum of two Fibonacci numbers close to a power of 2. In particular, he solved…”

“…in positive integers n, m and a with n ≥ m. Motivated by the above literature, we extend the work of [5] and [8] search for the sum of three Fibonacci numbers which are close to the power of 2. More specifically, we study the Diophantine inequality…”

“…Finally, we deal with the special cases where (n − m, n − l) ∈ {(0, 3), (1, 1), (1,5), (3, 0), (3,4), (4, 3), (5, 1), (7,8), (8, 7)}.…”