On polynomial solutions of Pell's equation (Q2666420)

Summary: Polynomial Pell's equation is \(x^2-D y^2=\pm1\), where \(D\) is a quadratic polynomial with integer coefficients and the solutions \(X\), \(Y\) must be quadratic polynomials with integer coefficients. Let \(D= a_2 x^2+ a_1x+ a_0\) be a polynomial in \(\mathbb{Z}[x]\). In this paper, some quadratic polynomial solutions are given for the equation \(x^2-D y^2=\pm1\) which are significant from computational point of view.