Repdigits base b as products of two Fibonacci numbers

被引：9

作者：

Erduvan, Fatih ^{[1
]}

Keskin, Refik ^{[1
]}

Siar, Zafer ^{[2
]}

机构：

[1] Sakarya Univ, Dept Math, Sakarya, Turkey

[2] Bingol Univ, Dept Math, Bingol, Turkey

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2021年 / 52卷 / 03期

关键词：

Fibonacci number; Repdigit; Diophantine equations; Linear forms in logarithms; Baker's Theory; SUMS; PELL;

D O I：

10.1007/s13226-021-00041-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (F-n) be the sequence of Fibonacci numbers defined by F-0 = 0, F-1 = 1, and F-n = Fn-1 + Fn-2 for n >= 2. Let 2 <= m <= n and b = 2, 3, 4, 5, 6, 7, 8, 9. In this study, we show that if FmFn is a repdigit in base b and has at least two digits, then FmFn is an element of {3, 4, 5, 6, 8, 9, 10, 13, 15, 16, 21, 24, 26, 40, 42, 63, 170, 273}. Furthermore, it is shown that if F-n is a repdigit in base b and has at least two digits, then (n, b) = (7, 3), (8, 4), (8, 6), (4, 2), (5, 4), (6, 3), (6, 7).

引用

页码：861 / 868

页数：8

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