For $n \in N^*$ we will say that the non-negative integers $x_1, x_2, ... , x_n$ have property $(P)$ if $$x_1x_2 ...x_n = x_1 + 2x_2 + 3x_3 + ...+ nx_n.$$ a) Show that for every $n \in N^*$ there exists $n$ positive integers with property $(P)$. b) Find all integers $n \ge 2$ so that there exists $n$ positive integers $x_1, x_2, ... , x_n$ with $x_1< x_2<x_3< ... <x_n$, having property $(P)$.