Construct all rational functions f (quotients of polynomials) in such that , where (f) is the divisor of the function f.
My answer/attempt: From my understanding of divisors, there seems to be exactly one function, namely, .
1.Are there any other functions with this divisor? If not, why?
2.If we restrict ourselves to divisors of rational functions only, then if we are given a divisor of a on , does there exists a unique rational function f with ?