The Biggest Degree

Algebra Level 4

Find the largest possible degree n1000n \le 1000 of a polynomial p(x)p(x) such that

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