The Biggest Degree

Algebra Level 5

Find the largest possible degree \(n \le 1000\) of a polynomial \(p(x)\) such that:

  1. \(p(i) = i \,\) for every integer \(i\) with \(1 \le i \leq n\)
  2. \(p(-1) = 1671\)
  3. \(p(0)\) is an integer (not necessarily 0).
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