Finding invertible polynomials in polynomial ring $\mathbb{Z}_{n}[x]$ 
Is there a method to find the units in $\mathbb{Z}_{n}[x]$? 

For instance, take $\mathbb{Z}_{4}$. How do we find all invertible polynomials in $\mathbb{Z}_{4}[x]$? Clearly $2x+1$ is one. What about the others? Is there any method?

HINT $\rm\ r_0 + r_1\ x +\:\cdots\: + r_n\ x^n\ $ is a unit in $\rm\:R[x]\:\ \iff\ r_0\:$ is a unit and $\rm\: r_i\: $ is nilpotent for $\rm\ i\ge 1\:.$
