Several Special Kinds Of Indeterminate Equations Study

Another name of indeterminate equation is Diophantine equation. Indeterminate equation is a very important research topics in the number theory.The achievements in indeterminate equations play an important role both in every branch of mathe-matics and in other subjects, such as physics, economics. So there are still many people have great interested in indeterminate equations.Indeterminate equation is an old problem, especially, it's more difficult to apply primary method to resolve the problems related to indeterminate equation. There are many solutions, which are very simple and also easy to understand, but hard to think out. In this paper primary and the supreme methods are utilized synthetically. the main contributions to several types of special indeterminate equation studies contain the following three aspects.1. The author first introduced the research progress of indeterminate equation x3±1=Dy2, and by using congruence and recursive sequence, proved that the indeterminate Equation x3-1= 65y2 has only the integer solution (x,y)=(1,0).2. Next the author introduced the recent progress of indeterminate equation x3±B=Dyn. Using the method of algebraic number theory, the author has studied integral solution of the indeterminate equation x3+13=y2.3. Finally the author introduced the recent progress of indeterminate equation Ax2+B=Cyn. Using the method of algebraic number theory, the author has studied integral solution of the indeterminate equation x2+4=y5 and the indeterminate equation x2+64=y5 and the indeterminate equation x2+64=y7...