# Victor's Level 5 Challenges - 1

Algebra Level 5

Find the greatest positive integer $$n$$ such that there are $$n$$ different real numbers $$x_1, x_2, \cdots, x_n$$ which satisfy the following inequality for any $$1 \leq i \leq j \leq n$$:

$100(1+x_i x_j)^2 \leq 99(1+x_i^2)(1+x_j^2).$

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