论文标题
关于卢卡斯序列的成员，这是加泰罗尼亚人数的产物
On members of Lucas sequences which are products of Catalan numbers
论文作者
论文摘要
We show that if $\{U_n\}_{n\geq 0}$ is a Lucas sequence, then the largest $n$ such that $|U_n|=C_{m_1}C_{m_2}\cdots C_{m_k}$ with $1\leq m_1\leq m_2\leq \cdots\leq m_k$,其中$ c_m $是加泰罗尼亚$ M $ th $ n <6500 $。如果卢卡斯序列的根是真实的，我们有$ n \ in \ {1,2、3、4、6、8、12 \} $。结果，我们表明，如果$ \ {x_n \} _ {n \ geq 1} $是pell方程的$ x $坐标的序列$ x^2-dy^2 = \ pm 1 $，则使用非noSquare Integer $ d> 1 $，然后是$ x_n = c_m $ $ $ $ $ $ n = 1 $ $ n = 1 $ n = 1 $ n = 1 $。
We show that if $\{U_n\}_{n\geq 0}$ is a Lucas sequence, then the largest $n$ such that $|U_n|=C_{m_1}C_{m_2}\cdots C_{m_k}$ with $1\leq m_1\leq m_2\leq \cdots\leq m_k$, where $C_m$ is the $m$th Catalan number satisfies $n<6500$. In case the roots of the Lucas sequence are real, we have $n\in \{1,2, 3, 4, 6, 8, 12\}$. As a consequence, we show that if $\{X_n\}_{n\geq 1}$ is the sequence of the $X$ coordinates of a Pell equation $X^2-dY^2=\pm 1$ with a nonsquare integer $d>1$, then $X_n=C_m$ implies $n=1$.
