The 3003rd element

Algebra Level 3

Let $$x_0, x_1, x_2,\ldots$$ be a sequence of real numbers satisfying the recursion,

$x_n = x_{n-1} + x_{n+1}$

for $$n = 1,2,3,\ldots$$.

If $$x_0 = 23$$, what is $$x_{3003}$$?

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