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ON THE TERNARY QUADRATIC DIOPHANTINE EQUATION 6z2 = 6x2 – 5y2

The ternary homogeneous quadratic equation given by 6z2 = 6x2 -5y2 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 are presented.