摘要Abstract

A Horadam sequence is a sequence generated by the second-order linear homogeneous recurrence relation $W_n=p{W}_{n-1}-q{W}_{n-2}; W_0=a, W_1=b$. The sequence of Fibonacci numbers is a particular case of a Horadam sequence. For any fixed integers $s$, $t$, and $k$, we investigate the boundedness and periodicity of the sequence $\left(\gcd \right(W_n+s, W_{n+k}+t\left)\right)$ in this paper.

荷拉德姆序列是由二階線性齊次遞迴關係式 $W_n=p{W}_{n-1}-q{W}_{n-2}; W_0=a, W_1=b$ 生成的序列。費波那契數列是荷拉德姆序列的一個特例。在這篇論文，對於任意給定整數 $s$、$t$、$k$，我們探討序列 $\left(\gcd \right(W_n+s, W_{n+k}+t\left)\right)$ 的有界性與週期性。