Problem 35

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

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

Find $a_{2014}$ .

Set .