On the Solvability and Special Solutions of Parametric Pell Equations - Osipov, Nikolai; Orlov, Nikita; Orlova, Irina (Computer Tools in Education, 2025)
The paper investigates a family of solutions of second-order parametric Pell equations of the general form: x2 −mx y + y2 = B, where m and B are some parameters. An optimal algorithm for solving such equations is found as an alternative to the traditional method. The proposed method allows not only to solve equations of this type for specific values of the parametersm and B, but also to investigate some equations of this class for solvability as a whole. In the particular case of equations of a special type, sequences of natural numbers are identified —the parameters of the equation, for which it is totally unsolvable.