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On balancing and Lucas-balancing numbers expressible as a product of two $k$-Lucas numbers | ||
| Journal of Algebra and Related Topics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 مرداد 1405 اصل مقاله (215.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.31948.1865 | ||
| نویسندگان | ||
| B. P. Tripathy1؛ U. K. Dutta2؛ B. K. Patel* 3 | ||
| 1Department of Mathematics, Government (SSD) Higher Secondary School, Tapovan, Bhubaneswar 751030, Odisha, India | ||
| 2Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar, Bhubaneswar 751024, Odisha, India | ||
| 3P. G. Department of Mathematics, Government Women's College, Sundargarh 770001, Sambalpur University, Odisha, India | ||
| چکیده | ||
| A positive integer $n$ is called a balancing number if $1 + 2 + \cdots + (n-1) = (n+1) + (n+2) + \cdots + (n+r)$ holds for some positive integer $r$. Then $r$ is called a balancer corresponding to the balancing number $n$. It is well known that if $n$ is a balancing number, then $8n^{2}+1$ is a perfect square, and its positive square root is called a Lucas-balancing number. For any integer $k \geq 2$, let $\{L_{n}^{(k)} \}_{n \geq -(k-2)}$ denote $k$-generalized Lucas sequence which starts with $0, \dots ,2,1$($k$ terms) where each next term is the sum of the $k$ preceding terms. In this paper, we look at all the balancing and Lucas-balancing numbers that can be represented as the product of two $k$-Lucas numbers. | ||
| کلیدواژهها | ||
| $k$-Lucas numbers؛ Balancing numbers؛ Lucas-balancing numbers؛ Linear forms in logarithms؛ Reduction method | ||
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آمار تعداد مشاهده مقاله: 5 تعداد دریافت فایل اصل مقاله: 1 |
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