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On Polynomial Solutions of Pell’s Equation

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  • Hasan Sankari
  • Ahmad Abdo
  • Marco Fontana

Abstract

Polynomial Pell’s equation is x2−Dy2=±1, where D is a quadratic polynomial with integer coefficients and the solutions X,Y must be quadratic polynomials with integer coefficients. Let D=a2x2+a1x+a0 be a polynomial in Zx. In this paper, some quadratic polynomial solutions are given for the equation x2−Dy2=±1 which are significant from computational point of view.

Suggested Citation

  • Hasan Sankari & Ahmad Abdo & Marco Fontana, 2021. "On Polynomial Solutions of Pell’s Equation," Journal of Mathematics, Hindawi, vol. 2021, pages 1-4, August.
    • Handle: RePEc:hin:jjmath:5379284
    DOI: 10.1155/2021/5379284
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