Provided are: a flame resistant polymer which is obtained by reacting polyacrylonitrile with amine and nitro compounds, the polyacrylonitrile being polymerized by aqueous suspension polymerization using a redox initiator and containing an S component at an amount of 3,000 µg/g or less; a polymer solution using the polymer; a flame resistant fiber using the polymer solution; a carbon fiber using the flame resistant fiber; and methods for producing the same. A PAN-based polymer in which both yarn producing properties and flame resistance are improved can be realized. Also provided are a polymer solution which is suitable for spinning using the polymer and a method for producing the same, a desirable flame resistant fiber using the polymer solution and a method for producing the same, and a desirable carbon fiber using the flame resistant fiber and a method for producing the same.