Algebraic Aspects of Solutions of the Pell Equation

This work shows that powers of any solution of the Pell Equation lead to new solutions of this Equation. The new solutions preserve the variable y and associates the power to the variable x. As otherwise required, the parameter D satisfies the quotient (x2 – 1)/y2. Furthermore, it is shown that the product of (different) solutions of the Pell Equation do not provide new solutions. Similarly, the average of any two different solutions of the Pell Equation does not constitute a new solution.