On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences
| Autor: | Ddamulira, Mahadi, Luca, Florian |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | The Ramanujan Journal, 2020 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11139-020-00278-7 |
| Popis: | Let $r\ge 1$ be an integer and ${\bf U}:=(U_{n})_{n\ge 0} $ be the Lucas sequence given by $U_0=0$, $U_1=1, $ and $U_{n+2}=rU_{n+1}+U_n$, for all $ n\ge 0 $. In this paper, we show that there are no positive integers $r\ge 3,~x\ne 2,~n\ge 1$ such that $U_n^x+U_{n+1}^x$ is a member of ${\bf U}$. Comment: Accepted manuscript |
| Databáze: | arXiv |
| Externí odkaz: |
|