by zdzdzd
Last Updated July 28, 2017 01:20 AM

I would like to find all $\beta \in \mathbf{R}_{>0}$ such that there exist a sequence $(x_i)_{i \in \mathbf{N}}$ such that : $$x_{n+2} = \sqrt{\beta x_{n+1}-x_n}, x_n > 0, \forall n$$

I really don't know how to proceed yet here is what I've noticed so far :

- $\beta = 1$ work because the sequence $x_0 = 1$, $x_1 = 2$, $x_2 = 1$ works
- if $\beta \in \mathbf{N}$ then we must have $\beta \mid (x_{n+2}^2+x_n)$

Updated April 09, 2017 04:20 AM

- Serverfault Query
- Superuser Query
- Ubuntu Query
- Webapps Query
- Webmasters Query
- Programmers Query
- Dba Query
- Drupal Query
- Wordpress Query
- Magento Query
- Joomla Query
- Android Query
- Apple Query
- Game Query
- Gaming Query
- Blender Query
- Ux Query
- Cooking Query
- Photo Query
- Stats Query
- Math Query
- Diy Query
- Gis Query
- Tex Query
- Meta Query
- Electronics Query
- Stackoverflow Query
- Bitcoin Query
- Ethereum Query