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

  • M. A. Gopalan Professor, Department of Mathematics, SIGC, Trichy-620002, Tamil Nadu, INDIA
  • S. Nandhini M.Phil Scholar, Department of Mathematics, SIGC, Trichy-620002, Tamil Nadu, INDIA
  • J. Shanthi Lecturer, Department of Mathematics, SIGC, Trichy-620002, Tamil Nadu, INDIA
Keywords: Ternary quadratic, integer solutions, figurate numbers, homogeneous quadratic, polygonal number, pyramidal numbers

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.

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Meena K,Gopalan MA, Vidhyalakshmi S ,Thiruniraiselvi N.Observations on the Ternary Quadratic Diophantine Equation 2 2 2 x 9y  50z .International Journal of Applied Research 2015; 1(2): 51-53

Published
2015-04-30
How to Cite
Gopalan, M., Nandhini, S., & Shanthi, J. (2015). ON THE TERNARY QUADRATIC DIOPHANTINE EQUATION 6z2 = 6x2 – 5y2. International Journal of Engineering Technologies and Management Research, 1(1), 14-22. https://doi.org/10.29121/ijetmr.v1.i1.2015.22