On the ternary quadratic diophantine equation 5(x2+y2)-2xy=20z2
M.A.Gopalan, T.Geetha, K.Hemalatha
The ternary homogeneous quadratic equation give by 5(x2+y2)-2xy=20z2 representing a cone is analyzed for its non-zero distinct integer solutions. A few interesting relations between the solutions and special polygonal and pyramided numbers are presented. Also, given a solution, formulas for generating a sequence of solutions based on the given solutions is presented.