International Research Journal of Education and Technology

            This paper deals with the problem of obtaining non-zero distinct integer solutions to the non-homogeneous binary quadratic equations with two unknowns y² = 35x² + 1. A few interesting properties among the solutions are given. The construction of second order Ramanujan Numbers is illustrated. Employing the linear combination among the solutions of the given equation, integer solutions for other choices of hyperbola & parabola and a few relations among special polygonal numbers are obtained.

Keywords: Binary quadratic, non-homogeneous quadratic, Pell equation, Positive

                       Pell equation, hyperbola