How can the product of two binary recurrences be constant?
Let $\omega$ denote an integer. This paper studies the equation $G_nH_n=\omega$ in the integer binary recurrences $\{G\}$ and $\{H\}$ satisfy the same recurrence relation. The origin of the question gives back to the more general problem $G_nH_n+c=x_{kn+l}$ where $c$ and $k\ge0,~l\ge0$ are fixed int...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática
2014-01-01
|
| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/19926 |
| Summary: | Let $\omega$ denote an integer. This paper studies the equation $G_nH_n=\omega$ in the integer binary recurrences $\{G\}$ and $\{H\}$ satisfy the same recurrence relation. The origin of the question gives back to the more general problem $G_nH_n+c=x_{kn+l}$ where $c$ and $k\ge0,~l\ge0$ are fixed integers, and the sequence $\{x\}$ is like $\{G\}$ and $\{H\}$. The case of $k=2$ has already been solved (\cite{KLSz}) and now we concentrate on the specific case $k=0$. |
|---|---|
| ISSN: | 0037-8712 2175-1188 |