# The closer you look, the less you see

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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