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

Abstract

In this paper, we find all Fibonacci and Lucas numbers written in the form 2 a + 3 b + 5 c + 7 d , in non-negative integers a , b , c , d , with 0 ≤ max { a , b , c } ≤ d .

Keywords

• Fibonacci
• Lucas
• linear form in logarithms
• continued fraction
• reduction method