Question 44
Given are sequences $\{x_n\}$ and $\{y_n\}$ by the following recurrent relations: $x_1 = 1$, $y_1 = 39$ and
$$
x_{n+1} = 23x_n + y_n + 2, \quad y_{n+1} = 551x_n + 24y_n + 64.
$$
Prove that $x_n$ is a perfect square for all positive integer $n$.
$$
x_{n+1} = 23x_n + y_n + 2, \quad y_{n+1} = 551x_n + 24y_n + 64.
$$
Prove that $x_n$ is a perfect square for all positive integer $n$.