Studying Pell's Equation by Using the Quadratic Orders (Latakia University Journal -Basic Sciences Series, 2018)
In this paper , we will study the ability to solve Pell's equation 14x2-âˆ†y2=N">  in the set 14Z">  , 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 of  14N">  and 14âˆ†">  .