Here is the question which could be quit difficult (but could be not):

Let $C$ be a field of complex numbers and $f \in C[x,y]$ be a polynomial such that there exist $g \in C[x,y]$ and $Jac(f,g) \in C^{*}$ i.e. determinant of Jacobian matrix of polynomials $f$ and $g$ is a nonzero constant. Question: Is it true that $f$ is irreducible?

Any comments are welcome!