# Be negative!

Algebra Level 4

Consider the function$\large f(x_1,\ldots ,x_n)=\sum_{k=1}^{n}x_k^2-x_1x_3-\sum_{k=2}^{n-1}x_kx_{k+1}$

where $$n\geq 3$$ and $$x_1,\ldots ,x_n$$ are real numbers. Find the smallest value of $$n$$ such that $$f$$ attains some negative values.

If you come to the conclusion that no such $$n$$ exists, enter 666.

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