So I have this statement that I'm supposed to prove and I cannot for the life of me figure out what parts I'm allowed to assume and what part I am expected to prove, here it is: The residue of an analytic function f at a singularity a ∈ ℂ is the uniquely determined complex number c, such that the function [tex]f(z) - \frac{c}{z-a}[/tex] admits a primitive in a punctured neighborhood of the point a. (end statement) I know I'm allowed to assume that f is analytic with a singularity at a, but beyond that I just can't tell if it's a biconditional I have to prove, or if it's just a conditional and if so which way. Thanks
I think if means prove two things. 1. The residue is a uniquely determined complex number c. 2. f(x) has the property stated.