Integers representable as differences of linear recurrence sequences (2008.00844v1)

Abstract: Let ${U_n}{n \geq 0}$ and ${V_m}{m \geq 0}$ be two linear recurrence sequences. We establish an asymptotic formula for the number of integers $c$ in the range $[-x, x]$ which can be represented as differences $ U_n - V_m$. In particular, the density of such integers is $0$.