REPDIGITS IN THE BASE b AS SUMS OF FOUR BALANCING NUMBERS

被引：6
|
作者：
Keskin, Refik [1 ]
Erduvan, Fatih [1 ]
机构：
[1] Sakarya Univ, Fac Sci & Arts, Dept Math, Esentepe Yerleskesi, TR-54187 Serdivan Sakarya, Turkey
来源：
MATHEMATICA BOHEMICA | 2021年 / 146卷 / 01期
关键词：
balancing number; repdigit; Diophantine equations; linear form in logarithms; PELL;
D O I：
10.21136/MB.2020.0077-19
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The sequence of balancing numbers (B-n) is defined by the recurrence relation B-n = 6B(n-1) - Bn-2 for n >= 2 with initial conditions B-0 = 0 and B-1 = 1. B-n is called the nth balancing number. In this paper, we find all repdigits in the base b, which are sums of four balancing numbers. As a result of our theorem, we state that if B-n is repdigit in the base b and has at least two digits, then (n, b) = (2, 5), (3, 6). Namely, B-2 = 6 = (11)(5) and B-3 = 35 = (55)(6).
引用
收藏
页码：55 / 68
页数：14
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