# A trip along Route 66

Algebra Level 5

$\large \begin{cases} {\displaystyle\sum_{k=1}^{66} a_{k} = 2015} \\ {\displaystyle\sum_{k=1}^{66} a_{k}^{2} = 62465} \end{cases}$

Suppose real numbers $$a_1, a_2, a_3, \ldots,a_{66}$$ satisfy the two equations above with $$S = \max(a_1, a_2, a_3, \ldots, a_{66})$$.

If $$S = \dfrac{m}{n},$$ where $$m$$ and $$n$$ are positive coprime integers, then find $$m + n.$$

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