Looks complicated

Algebra Level pending

Find the minimum value of \(\displaystyle\sum_{k=1}^{2014} a_k^{2014} + \sum_{k=1}^{2014} \frac1{a_k^{2014}}\) where \(a_1, a_2, \cdots, a_{2014} > 0\).

Inspired by Calvin's comment on one of the solutions of this post

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