In this paper,structured of generative function method and technique is introduced by finding the solution of a kind of diophantus equation,thus we introduce power series such as generative function to apply in combination probabicity.

On the Diophantine equation x~p-1=Dy~n;

On the solution of the Diophantine equations x~2-2p=y~n;

On the Diophantine equation(15n)~x+(112n)~y=(113n)~z;

On the Diophantine equations x~4±y~6=z~2 and x~2+y~4=z~6;

When p is a odd prime and p ≠1 (mod 8), we get all solutions of diophantine equations ( x(x+1)(2x+1)=2p~ky~(2n) ) with elementary theory of number.

With the help of the elementary theory of number and Fermat method of infinite descent,some necessary conditions have been proved provided that the Diophantine equations x 4+mx 2y 2+ny 4=z 2 has positive Integer solutions that fit (x,y) =1 m.

Let p>3 be a prime integer prime,when the elementary grade method and the Diophantus Equation theories are used.

In this paper two theorems are given by using matrixvector description of polynomial multiplication, which are useful to resolve the Diophantus equation.