Repdigits as Sums of Four Tribonacci Numbers

被引：0

作者：

Zhou, Yuetong ^{[1
]}

Yang, Peng ^{[1
]}

Zhang, Shaonan ^{[1
]}

Zhang, Kaiqiang ^{[1
]}

机构：

[1] Univ Sci & Technol Liaoning, Sch Sci, Anshan 114051, Peoples R China

来源：

SYMMETRY-BASEL | 2022年 / 14卷 / 09期

关键词：

tribonacci numbers; repdigits; diophantine equations; Binet's formula; linear form in logarithms; FIBONACCI;

D O I：

10.3390/sym14091931

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we show that 66666 is the largest repdigit expressible as the sum of four tribonacci numbers. We used Binet's formula, Baker's theory, and a reduction method during the proving procedure. We also used the periodic properties of tribonacci number modulo 9 to deal with three individual cases.

引用

页数：15

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