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 ≤ max{a, b, c} ≤ 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