Question 94
For which values of $n \gt 1$ is there a set of pairwise distinct natural numbers $(a_1, a_2, ..., a_n)$ such that the following condition is satisfied:
$$
(a_1+1)!+(a_2+1)!+...+(a_n+1)! : a_1!+a_2!+...+a_n!
$$
$$
(a_1+1)!+(a_2+1)!+...+(a_n+1)! : a_1!+a_2!+...+a_n!
$$