Vol. 6, Issue 5, Part C (2020)

Abstract
The hyperbola represented by the binary quadratic equation (known as positive pellian equation) 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. Also, employing the solutions of the given equation, special Pythagorean triangle is constructed. The formulation of second order Ramanujan Numbers with base numbers as real integers and Gaussian integers is illustrated.