Let $p(x)$ be a polynomial of degree 4 such that $p(55) = p(83) = p(204) = p(232) = 8$ and $p(103) = 13.$  Find
\[p(1) - p(2) + p(3) - p(4) + \dots + p(285) - p(286).\]
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<|im_start|>user
Let $p(x)$ be a polynomial of degree 4 such that $p(55) = p(83) = p(204) = p(232) = 8$ and $p(103) = 13.$  Find
\[p(1) - p(2) + p(3) - p(4) + \dots + p(285) - p(286).\]
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<|im_start|>assistant

user
0
Let $p(x)$ be a polynomial of degree 4 such that $p(55) = p(83) = p(204) = p(232) = 8$ and $p(103) = 13.$  Find
\[p(1) - p(2) + p(3) - p(4) + \dots + p(285) - p(286).\]
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