Lattice Points on the Cone X^2+9Y^2=50Z^2

P. Jayakumar, K. Sangeetha

Abstract: The ternary quadratic homogeneous equation representing cone given by x^2+9y^2=50z^2 is analyzed for its non- zero distinct integer points on it. 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: Diophantine equation, Ternary quadratic, integral solutions, special numbers, a few interesting Relation