Question 34
Let $n$ be a nonnegative integer and $M = \{n^3, n^3 + 1, n^3 + 2, \dots, n^3 + n\}$. Consider $A$ and $B$ two nonempty, disjoint subsets of $M$ such that the sum of elements of the set $A$ divides the sum of elements of the set $B$. Prove that the number of elements of the set $A$ divides the number of elements of the set $B$.