# Removing the Obvious

Number Theory Level 3

Does there exist a multi-set $$A = \{ a_1, a_2, \ldots , a_{2016} \}$$ of positive integers such that

• $$\sum a_i ^3 = (\sum a_i)^2$$
• $$A \neq \{ 1, 2, \ldots , 2016 \}$$
• $$a_1 \neq a_2?$$

Note: Multi-set means that the elements could be repeated.

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