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

Algebra Level 5

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

  1. f(x)f(x) is a monic polynomial;
  2. f(x)f(x) has degree 10001000;
  3. f(x)f(x) has integer coefficients;
  4. f(x)f(x) divides f(2x3+x)f(2x^3+ x).
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