In this study, we find all Fibonacci and Lucas numbers which can be expressible as a product of two repdigits in the base b. It is shown that the largest Fibonacci and Lucas numbers which can be expressible as a product of two repdigits are \(F_{12}=144\) and \(L_{15}=1364\), respectively. Also, we have the presentation

$$\begin{aligned} F_{12}=144=6\times (3+3\cdot 7)=(6)_{7}\times (33)_{7}=4\times (4+4\cdot 8)=(4)_{8}\times (44)_{8} \end{aligned}$$

and

$$\begin{aligned} L_{15}=1364\times (22222)_{4}=2\times (2+2\cdot 4+2\cdot 4^{2}+2\cdot 4^{3}+2\cdot 4^{4}). \end{aligned}$$

中文翻译：

---

Fibonacci或Lucas数是基数b中两个Repdigits的乘积

在这项研究中，我们找到了所有可表示为以b为基的两个表示数字的乘积的斐波那契数和卢卡斯数。结果表明，可以表示为两个数字的乘积的最大斐波那契数和卢卡斯数分别为\（F_ {12} = 144 \）和\（L_ {15} = 1364 \）。另外，我们有演讲

$$ \ begin {aligned} F_ {12} = 144 = 6 \ times（3 + 3 \ cdot 7）=（6）_ {7} \ times（33）_ {7} = 4 \ times（4 + 4 \ cdot 8）=（4）_ {8} \次（44）_ {8} \ end {aligned} $$

和

$$ \ begin {aligned} L_ {15} = 1364 \ times（22222）_ {4} = 2 \ times（2 + 2 \ cdot 4 + 2 \ cdot 4 ^ {2} +2 \ cdot 4 ^ {3 } +2 \ cdot 4 ^ {4}）。\ end {aligned} $$