If ℤ[x] denotes the commutative ring consisting of all polynomials with integer coefficients, list all the elements in ℤ[x] that have a multiplicative inverse in ℤ[x].
Multiplicative inverse if rs = 1 where rs ∈ R (rs are elements of the ring).
Polynomials are of the form a_n*x^n+a_(n-1)*x^(n-1)+...+a_1*x+a_0
in this case, the a coefficients are all integers.
The Attempt at a Solution
At first glance, this is an overwhelming question. They want me to list ALL the elements that have a multiplicative inverse?
This fact leads me to believe that there is, in fact, a very special rule for this to occur which limits the amount that can be inverses OR they just want a general rule.
Yeah, I'm really lost on this one.
I realize I don't have much of an answer here, so I am not looking for a big hint yet. I know PF policy is to show your work prior to help.
Just give me something to get me going...