A Pillai-Catalan-type problem involving Fibonacci numbers

Seyran S. Ibrahimov; Nazim I. Mahmudov

doi:10.1007/s41478-024-00779-4

paper

A Pillai-Catalan-type problem involving Fibonacci numbers

arXiv:2401.08205 · doi:10.1007/s41478-024-00779-4

Abstract

This paper addresses A Pillai-Catalan-type problem assosiated with Fibonacci numbers. Let $F_{n}$ be the Fibonacci numbers defined by the recurrence relation $F_{1} = 1$ , $F_{2} = 1$ and $F_{n} = F_{n - 1} + F_{n - 2}$ for all $n \geq 3$ . We will find all positive integer solution to the equation $3^{x} - F_{n} 2^{y} = 1$ using properties of Fibonacci numbers, linear forms of logarithms, and the Baker-Davenport reduction method.

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