On Ternary Quadratic Homogeneous Diophantine Equation 5x2 + 5y2 ? 9xy = 20z2

Dr. P. Jayakumar, S. Prabha

Abstract: Five different methods of the non-zero integral solutions of the ternary quadratic homogeneous Diophantine equation 5x2 + 5y2 9xy =20z2 are obtained. Some interesting relations among the special numbers and the solutions are exposed.

Keywords: Ternary Quadratic, homogenous cone, integer solutions, special numbers