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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