Bulletin of Pure and Applied Sciences Section.
  • Year: 2019
  • Volume: 38E
  • Issue: 1

On the Homogeneous Cone 3x2 – 8y2 = 25z2

1Professor, Department of Mathematics, SIGC, Trichy, Tamil Nadu620002, India.

2M.Phil Scholar, Department of Mathematics, SIGC, Trichy, Tamil Nadu620002, India

*Sharadha Kumar, M.Phil Scholar, Department of Mathematics, SIGC, Trichy, Tamil Nadu 620002, India. E-mail: sharadhak12@gmail.com

**E-mail: mayilgopalan@gmail.com

Abstract

This paper aims at determining non-zero distinct integer solutions satisfying the homogeneous cone represented by the ternary quadratic equation 3x2 – 8y2 = 25z2 . A few interesting relations among the solutions are presented. A general formula for generating sequence of integer solutions to the given cone based on a given solution is illustrated.

Keywords

Ternary quadratic, homogeneous quadratic, homogeneous cone, integer solutions, 11D09