Question 66
Let $n \gt 2$ be a natural number. Prove that the following equation has no solution $x_1, x_2, \dots, x_n$ in positive integers numbers greater than 1:
$$
(x_1x_2\dots x_n)^2 = x_1^3 + x_2^3 + \dots + x_n^3
$$
$$
(x_1x_2\dots x_n)^2 = x_1^3 + x_2^3 + \dots + x_n^3
$$