Solvability of both Diophantine equations kX^2+2lXY-2kY^2=±1 and X^2-mY^2=-2 - Sankari, Hasan (Latakia University Journal -Basic Sciences Series, 2019)
In this research, we investigate solving both of Diophantine equations in the title of research in . If is a prime number, then both of Diophantine equations are solvability if and only if one of them is solvability, and we find conditions to make one of equations solvability if and only if the other is solvability, and use the solution of one to find the solution of other. Besides of determine conditions to solvability of the Pell’s equation and one case of generalizations Pell’s equation, and we find relation of main solution of Pell’s equation and other case of generalization Pell’s equation. Adding of them we prove some results about solution of Pell’s equation, where is an odd number.