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

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 $f(2x^3+ x)$.
×