# More fun with quadratic forms

Algebra Level 5

Find the smallest positive integer $$n$$ such that there exist real numbers $$x_0,x_1,\ldots,x_n$$ with $$\displaystyle \sum_{k=0}^{n}x_k^2=1$$ and $$\displaystyle \sum_{k=1}^{n}x_0x_k>1$$.

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

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