Lattice Points on the Homogeneous Cone x2+y2= 26z2

Dr. P. Jayakumar, R. Venkatraman

Abstract: The ternary quadratic homogeneous equation representing cone is considered and analyzed for finding its non zero distinct integral solutions. Five different patterns of integer points satisfying the cone under consideration are obtained. A few interesting relation between the solutions and special number patterns are presented.

Keywords: Homogeneous cone, Ternary Quadratic, Integral solutions, special numbers Homogeneous cone, Ternary Quadratic, Integral solutions, special numbers