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Algebra Level 5

Let \(p(x)\) and \(q(x)\) be \(2557^{th}\) degree polynomials which satisfy the system of equations:

\[\begin{cases} p(n) = q(n)\text{ for }n = 1, 2, 3, \cdots, 2557\\ p(2558) = q(2558) +1. \end{cases}\]

Find \(p(0) - q(0).\)

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