دراسة قابلية حل المعادلتين X2-ΔY2=-3 و aX2+2bXY-3aY2=±1

Abstract EN

The aim of this article is studying the equations aX2+2bXY-3 aY2 = ±1 (I) and X 2-Δ Y2 =-3 (II), we proved that if equation (II) is unsolvable then the equation (I) is unsolvable, also we proved necessary and sufficient condition such that the equation (I) is solvable when the equation (I) is solvable, and we proved necessary and sufficient condition such that the equation (I) is solvable when the equation (II) is solvable.

We proved that if is prime number then the equation (I) is solvable iff the equation (II) is solvable.