On $k$-Fibonacci balancing and $k$-Fibonacci Lucas-balancing numbers
The balancing number $n$ and the balancer $r$ are solution of the Diophantine equation $$1+2+\cdots+(n-1) = (n+1)+(n+2)+\cdots+(n+r). $$ It is well known that if $n$ is balancing number, then $8n^2 + 1$ is a perfect square and its positive square root is called a Lucas-balancing number. For an integ...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2021-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/4410 |