Abstract
The binary quadratic equation represented by the negative pellian y2=45x2-11 is analyzed for its distinct integer solutions. A few interesting relations among the solutions are also given. Further, employing the solutions of the above hyperbola, we have obtained solutions of other choices of hyperbolas, parabolas and special Pythagorean triangle.
Highlights
Observations: From the above table, we observe some interesting relations among the solutions which are presented below
Employing linear combinations among the solutions of (1), one may generate integer solutions for other choices of hyperbolas which are presented in the table 1 below
Employing linear combinations among the solutions of (1), one may generate integer solutions for other choices of parabolas which are presented in the table 2 below
Summary
METHOD OF ANALYSIS: The negative pell equation representing hyperbola under consideration is y 2 45x2 11. Applying Brahamagupta Lemma[16] between x0 , y0 and ~xn, ~yn , the other integer solutions of (1). Observations: From the above table, we observe some interesting relations among the solutions which are presented below
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