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arXiv · 2008.00844

Integers representable as differences of linear recurrence sequences

Robert Tichy·Ingrid Vukusic·Daodao Yang·Volker Ziegler
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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 $0$.

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Robert Tichy, Ingrid Vukusic, Daodao Yang, Volker Ziegler. 2020-08-03. Integers representable as differences of linear recurrence sequences. https://arxiv.org/abs/2008.00844

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