On a variant of Pillai's problem II

TL;DR

This paper proves that for certain linear recurrence sequences, only finitely many constants c allow the equation U_n - V_m = c to have multiple solutions, extending understanding of recurrence differences.

Contribution

It establishes finiteness results for the number of constants c with multiple solutions in the difference of two linear recurrence sequences.

Findings

Finitely many c have multiple solutions for U_n - V_m = c

Results extend previous work on recurrence difference equations

Provides new bounds and conditions for solution finiteness

Abstract

In this paper, we show that there are only finitely many $c$ such that the equation $U_n - V_m = c$ has at least two distinct solutions $(n,m)$, where $\{U_n\}_{n\geq 0}$ and $\{V_m\}_{m\geq 0}$ are given linear recurrence sequences.