with integer coefficients, we can find polynomials by looking at the cyclotomic polynomials.
What are the general characteristics of complex number and real number coefficients polynomials which satisfy that $f(x)|f(x^2)$. Do we have some methods to count them or find them?
For example, $f(x)=(x-i)(x-1)(x+1)$satisfies this property. Also the $x^4+x^3+x^2+x+1$
