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:
- \(f(x)\) is a monic polynomial,
- \(f(x)\) has degree \(1000\),
- \(f(x)\) has integer coefficients,
- \(f(x)\) divides \(f(2x^3+ x)\).