On a problem of Pillai with Fibonacci numbers and powers of 2

TL;DR

This paper investigates integers that can be expressed as the difference between a Fibonacci number and a power of 2 in at least two different ways, aiming to classify all such integers.

Contribution

The paper completely characterizes all integers with multiple representations as Fibonacci number minus power of 2 differences.

Findings

Identifies all integers with multiple representations

Provides a complete classification of solutions

Advances understanding of Fibonacci and powers of 2 differences

Abstract

In this paper, we find all integers c having at least two representations as a difference between a Fibonacci number and a power of 2.