# 2018-04 An inequality

Let $$x_1,x_2,\ldots,x_n$$ be reals such that $$x_1+x_2+\cdots+x_n=n$$ and $$x_1^2+x_2^2+\cdots +x_n^2=n+1$$. What is the maximum of $$x_1x_2+x_2x_3+x_3x_4+\cdots + x_{n-1}x_n+x_nx_1$$?

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