Integers representable as differences of linear recurrence sequences

Let $\{U_n\}_{n \geqslant 0}$ and $\{G_m\}_{m \geqslant 0}$ be two linear recurrence sequences defined over the integers. We establish an asymptotic formula for the number of integers $c$ in the range $[-x, x]$ which can be represented as differences $U_n - G_m$, when $x$ goes to infinity. In particular, the density of such integers is $0$.

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