On The Diophantine Equation Kx~2-ly~2=4

Stormer's theorem is that if(x,y)is a positive integer solution of Pell's equation x2-Dy2=±1,in which D>0 is a non-square integer and all prime factors of y divide D,the conclusion is that(x,y)is the basic solution of the Pell equation x2-Dy2=±1.In this paper,by using Stormer's theorem with its extension,and the properties of Lehmer's sequence with its adjoint sequence,we discuss the Diophantine equation kx2-ly2=4Let(?),this paper proves the relationship between the positive integer solution(x,y)and the minimum solution ? when x(y)has a prime factor not dividing k(l)and when x(y)has two prime factor not dividing k(l).And this theorems is applied to obtain some concrete examples.