Question 63
Find the smallest positive integer $N$ for which the equation
$$(x^2 - 1)(y^2 - 1)(z^2 - 1) = N$$
has at least two different integer solutions $(x, y, z)$ satisfying $1 \lt x \le y \le z$.
$$(x^2 - 1)(y^2 - 1)(z^2 - 1) = N$$
has at least two different integer solutions $(x, y, z)$ satisfying $1 \lt x \le y \le z$.