Fibonacci and Lucas Numbers of the Form $-2^a-3^b-5^c+7^d$

Abstract

In this note we find all Fibonacci and Lucas numbers of the form $-2^a-3^b-5^c+7^d$ where $a, b, c, d$ are non-negative integers, with $0 \leq \max\{a, b, c\}\leq d$. This result gives an answer to a question posed by Qu, Zeng and Cao.

Keywords

• Fibonacci and Lucas sequences
• Linear form in logarithms
• reduction method