论文标题
整数可表示为线性复发序列的差异
Integers representable as differences of linear recurrence sequences
论文作者
论文摘要
令$ \ {u_n \} _ {n \ geqslant 0} $和$ \ {g_m \} _ {m \ geqslant 0} $为在整数上定义的两个线性复发序列。我们为整数$ c $ $ c $在$ [ - x，x] $中的渐近公式建立，当$ x $转到无限时，可以表示为差异$ u_n -g_m $。特别是，此类整数的密度为$ 0 $。
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 $0$.
