Power Mean Inequalities

Algebra Level 3

\[ \large\frac {a_{1}^2 + 4}{a_1} + \frac {a_{2}^2 + 4}{a_2} + \cdots + \frac {a_{n}^2 + 4}{a_n} \geq 2017 \]

Find the least positive integer value of \(n\) such that for any \(n\) positive reals \(a_{1}, a_{2}, \ldots , a_{n}\), the inequality above is satisfied.

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