Observations on Pell-like Equation 11x²-6y²=-10

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Shreemathi Adiga

Observations on Pell-like Equation 11x²-6y²=-10

Keywords : Binary quadratic, Hyperbola, Parabola, Pell equation, Integral solutions


Abstract

This paper concerns with the problem of finding non-zero distinct integer solutions to the Pell-like equation represented by 11x²-6y²=-10. 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. Also, employing the solutions of the given equation, special Pythagorean triangle is constructed.

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