CMO 2010 Problem 3

Suppose $a_1,a_2,a_3,b_1,b_2,b_3$ are distinct positive integers such that $$(n + 1)a_1^n + na_2^n + (n - 1)a_3^n|(n + 1)b_1^n + nb_2^n + (n - 1)b_3^n$$ holds for all positive integers $n$ . Prove that there exists $k\in N$ such that $b_i = ka_i$ for $i = 1,2,3$ .