Question 151
For which positive integers $n$ there exist $2n$ pairwise different positive integers $a_1, a_2, \dots, a_n$ and $b_1, b_2, \dots, b_n$ satisfying the equations:
$$
a_1 + a_2 + \dots + a_n = b_1 + b_2 + \dots + b_n \text{ and } a_1 a_2 \dots a_n = b_1 b_2 \dots b_n?
$$
$$
a_1 + a_2 + \dots + a_n = b_1 + b_2 + \dots + b_n \text{ and } a_1 a_2 \dots a_n = b_1 b_2 \dots b_n?
$$