Question 128
The sequence $\{x_n\}_{n \geq 1}$ is defined as follows: $x_1 = x_2 = 1$ and $x_{n+2} = x_{n+1} + x_n + 2\sqrt{x_{n+1} x_n + 3}$ for all $n \geq 1$. Prove that $x_n$ is integer for all $n \geq 2$.
(proposed by Bat. Bayarjargal)
(proposed by Bat. Bayarjargal)