Abstract
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.
Highlights
The Diophantine equations offer an unlimited field for research due to their variety [1-3].In particular, one may refer [4-24] for quadratic equations with three unknowns
This communication concerns with yet another interesting equation 6z2 6x2 - 5y2 representing non-homogeneous quadratic equation with three unknowns for determining its infinitely many non-zero integral points
As the considered equation is symmetric in x, y and z, we have presented only positive integer solutions for clear understanding
Summary
“On the Ternary Quadratic Diophantine Equation 6z2 = 6x2 – 5y2.”. International Journal of Engineering Technology and Management Research, Vol 1, No 1(2015): 14-22.
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