Given that m,n are positive numbers and given that A_1, A_2, \ldots, A_m \subseteq{\{1,2,\ldots,n\}} such that A_i \neq A_j for i \neq j.

We know that \exists a constant L such that for every i\neq j:

\sum_{x\in A_i \cap A_j}{x^3 = L}

Prove m \leq n