# Problem 35

Algebra Level 5

$$\left\{\begin{matrix} a_{1}+a_{2}+a_{3}+\cdots+a_{2014}\geq 2014^2 & & \\a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+\cdots+a_{2014}^{2}\leq 2014^3+1 & & \end{matrix}\right.$$.

Given $$a_{1},a_{2},\ldots, a_{2014}$$ and they are natural number that satisfy the inequalities above.

Find $$a_{2014}$$.

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