On a variant of Pillai's problem

TL;DR

This paper investigates integers that can be expressed as the difference between a Fibonacci and a Tribonacci number in at least two different ways, expanding understanding of their combinatorial properties.

Contribution

It characterizes all integers with multiple representations as differences between Fibonacci and Tribonacci numbers, a novel extension of Pillai's problem.

Findings

Identifies all such integers with multiple representations

Provides a complete classification of these integers

Advances the understanding of Fibonacci-Tribonacci difference representations

Abstract

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