Abstract:
This thesis presents a classification of some cases of generalized Fermat equation and applications of elementary methods to these equations in order to find integer solutions to these equations. Applications of some more recent and advanced methods for some equations where elementary methods do not work are also presented. The classification consists of three cases. The solution sets of equations in the first two cases are completely determined. The third case where Fermat equation is included still contains unsolved problems. Applications of elementary methods to some of the equations in this case and some open problems related to this case are presented in the last chapter of the thesis.
