.U(Z_4) ={ 1, 3}. Z_4 is integers mod n

In general, U(Z_n) = { a in Z_n: hcf(a,n) =1}

And

U(Z_4[X]) = { 0, 1, 2 ,3}. Is this correct?

Nop. In general, , when R is a ring, so in this case the units of the polynomial ring are the same as the ring's.

Tonio

where Z_n[X] is polynomial ring over Z generated by one variable

How do you generate the formula of U(Z_n[X])?

Thank you