Question 87
Let $k \ge 2$ be an integer. Prove that for each positive integer $N \lt 40 \cdot 3^k$ the equation
$$
(x_1^2 - 1)(x_2^2 - 1) \cdots (x_k^2 - 1) = N
$$
has at most one integer solution $(x_1, x_2, \dots, x_k)$ such that $1 \lt x_1 \le x_2 \le \dots \le x_k$.
$$
(x_1^2 - 1)(x_2^2 - 1) \cdots (x_k^2 - 1) = N
$$
has at most one integer solution $(x_1, x_2, \dots, x_k)$ such that $1 \lt x_1 \le x_2 \le \dots \le x_k$.