This nal project discusses the solutions for a diophantine equation { A + B = C, ABC = Dn, where A, B, C, D, n are positive integers and n ≥ 3. The equations are regard as a generalization of Fermat's equation xn +yn = zn. This is a review of some parts of Cai et al. [Journal of Number Theory, 149 (2015), 33{45]. The solutions are determined by using the concept of greatest common div…