论文标题
斐波那契和卢卡斯数字是基本$ g $的三个股票的产品
Fibonacci and Lucas numbers as products of three repdigits in base $g$
论文作者
论文摘要
回想一下，基本$ g $中的repdigit是一个正整数，其基础$ g $扩展中只有一个数字，即，对于某些正整数$ a（g^m-1）/（g^m-1）/（g^m-1）/（g^m-1）/（g-1）$，对于某些积极的整数$ m \ geq 1 $，$ g \ geq 2 $ and $ g \ geq 2 $ and $ 1 \ leq a \ leq a \ leq g-1 $。在本研究中，我们调查了所有斐波那契或卢卡斯的数字，这些数字表示为基础$ g $的三个折叠产品。作为例证，我们考虑了$ g = 10 $的情况，其中我们表明数字144和18是最大的斐波那契和卢卡斯的数字，可以分别作为三种repdigits的产品表达。所有这些都可以使用代数数的对数中的线性形式完成。
Recall that repdigit in base $g$ is a positive integer that has only one digit in its base $g$ expansion, i.e. a number of the form $a(g^m-1)/(g-1)$, for some positive integers $m\geq 1$, $g\geq 2$ and $1\leq a\leq g-1$. In the present study we investigate all Fibonacci or Lucas numbers which are expressed as products of three repdigits in base $g$. As illustration, we consider the case $g=10$ where we show that the numbers 144 and 18 are the largest Fibonacci and Lucas numbers which can be expressible as products of three repdigits respectively. All this can be done using linear forms in logarithms of algebraic numbers.
