Question 40
Let $n$ be a positive integer. Find all $n$-tuples $(a_1, a_2, \dots, a_n)$ of distinct positive integers such that
$$
\frac{(a_1+d)(a_2+d)\dots(a_n+d)}{a_1 a_2 \dots a_n}
$$
is an integer for every integer $d \ge 0$.
$$
\frac{(a_1+d)(a_2+d)\dots(a_n+d)}{a_1 a_2 \dots a_n}
$$
is an integer for every integer $d \ge 0$.