Question 80
Determine all arithmetic sequences $a_{1}, a_{2}, \ldots$ for which there exists integer $N\gt 1$ such that for any positive integer $k$ the following divisibility holds
$$
a_{1} a_{2} \ldots a_{k} \mid a_{N+1} a_{N+2} \ldots a_{N+k} .
$$
$$
a_{1} a_{2} \ldots a_{k} \mid a_{N+1} a_{N+2} \ldots a_{N+k} .
$$