Discussion And Research About The Integer Solutions Of Diophantine Equations

Number theory is a very important branch of mathematics, which develop rapidly, and is widely used in the development of other subjects. In this paper, a class of the Diophantine equation with the form x3±n3= Ay2 has been discussed. The thesis contains three parts, the main ideas as follows:The first chapter briefly elaborates the overview, the achievements and the status of the Diophantine equation, and also states the main achievements of the thesis.The second chapter introduces the process of solving the Diophantine equa-tion, also proves some conclusions about the Diophantine equation x3±n3= Ay2 with no positive integer solution.The third chapter elaborates a rigorous proof to achieve some conclusions about the equations with no positive integer solution.