Inspired by Aareyan Manzoor, again

Algebra Level 4

\[S=\large \sum_{k=1}^{2016}x_kx_{k+1}\]

Find the maximum of \(S\) if \(\displaystyle \sum_{k=1}^{2016}x_k^2=2016\) and \(x_{2017}=x_1\).


Inspiration.

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