It isn't easy for f(x) to divide f(2x^3+x)

Algebra Level 5

Find the number of polynomials \(f(x)\) that satisfy all of the following conditions:

  1. \(f(x)\) is a monic polynomial;
  2. \(f(x)\) has degree \(1000\);
  3. \(f(x)\) has integer coefficients;
  4. \(f(x)\) divides \(f(2x^3+ x)\).
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