Balancing Numbers as Sum of Same Power of Consecutive Balancing Numbers

被引：1

作者：

Nansoko, Souleymane ^{[1
]}

Tchammou, Euloge ^{[1
]}

Togbe, Alain ^{[2
]}

机构：

[1] Inst Math & Sci Phys, Dangbo, Benin

[2] Purdue Univ Northwest, Dept Math Stat & Comp Sci, 1401 S,US 421, Westville, IN 46391 USA

来源：

VIETNAM JOURNAL OF MATHEMATICS | 2024年 / 52卷 / 01期

关键词：

Balancing numbers; Pell numbers; Linear form in logarithms; Reduction method; LOGARITHMS; FIBONACCI;

D O I：

10.1007/s10013-022-00573-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we find all the balancing numbers which are sum of same power of consecutive balancing numbers. For this, we find all the solutions of the Diophantine equation B-n(x) + B-n+1(x) + ... + B-n+k-1(x) = B-m in positive integers (m, n, k, x), where B-i is the i th term of the n n balancing sequence.

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页码：75 / 88

页数：14

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