Question 106
Let $k$ be a positive integer. Determine all $k$-tuples $(n_1, n_2, ..., n_k)$ of positive integers such that
$$(n_1! - 1)(n_2! - 1) \cdots (n_k! - 1) - 16$$
is a perfect square of a positive integer.
$$(n_1! - 1)(n_2! - 1) \cdots (n_k! - 1) - 16$$
is a perfect square of a positive integer.