On the Positive Pellian Equation y2 = 48x2 + 16

Shreemathi Adiga; N. Anusheela; M.A. Gopalan

doi:https://doi.org/10.14445/22315373/IJMTT-V59P536

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 59 | Number 4 | Year 2018 | Article Id. IJMTT-V59P536 | DOI : https://doi.org/10.14445/22315373/IJMTT-V59P536

On the Positive Pellian Equation y2 = 48x2 + 16

Shreemathi Adiga , N. Anusheela, M.A. Gopalan

Citation :

Shreemathi Adiga , N. Anusheela, M.A. Gopalan, "On the Positive Pellian Equation y2 = 48x2 + 16," International Journal of Mathematics Trends and Technology (IJMTT), vol. 59, no. 4, pp. 256-264, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V59P536

Abstract

The hyperbola represented by the binary quadratic equation y2 = 48x2 + 16 is analyzed for finding its non-zero distinct integer solutions. A few interesting relations among its solutions are presented. Also, knowing an integral solution of the given hyperbola, integer solutions for other choices of hyperbolas and parabolas are presented. Employing the solutions, a special Pythagorean triangle is constructed.

Keywords

Binary quadratic, Hyperbola, Parabola, Pell equation, Integral solutions.

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