Question 99
The sequence $\{x_n\}$ is given by $x_0=a,x_1=2$ and
$$2x_n-1=2x_{n-1}x_{n-2}-x_{n-1}-x_{n-2}+1.$$
Find all $a$ for which $2x_{3n}-1$ is the square of an integer.
$$2x_n-1=2x_{n-1}x_{n-2}-x_{n-1}-x_{n-2}+1.$$
Find all $a$ for which $2x_{3n}-1$ is the square of an integer.