In this work, we studied Pell equations X2 - DY2 = ±2. We showed when both
of these equations are solvable, and we found the necessary and sufficient
condition for the solubility of each one by the continued fractions and the
concept of the central norm.
In this paper , we will study the ability to solve Pell's equation in the
set Z, we give necessary and sufficient conditions to solve this equation , depending on the
ideals in orders of the real quadratic fields .We also introduce the formula of the opposite
ideal for every solution of this equation , in special cases.
