International Journal of Engineering, Science and Mathematics
  • Year: 2014
  • Volume: 3
  • Issue: 2

On homogeneous ternary quadratic diophantine equation: 2(x2+y2)-3xy=16z2

  • Author:
  • K. Meena, S. Vidhyalakshmi, M.A. Gopalan, S. Aarthy Thangam
  • Total Page Count: 7
  • Page Number: 63 to 69

*Former VC, Bharathidasan University, Trichy-620 024, Tamil Nadu, India

**Professor, Department of Mathematics, Shrimati Indira Gandhi College, Trichy-620 002, Tamil Nadu, India

***M.Phil student, Department of Mathematics, Shrimati Indira Gandhi College, Trichy-620 002, Tamil Nadu, India

2010 Mathematics Subject Classification: 11D09

Abstract

The ternary quadratic homogeneous equation representing homogeneous cone given by 2(x2+y2)-3xy=16z2 is analyzed for its non-zero distinct integer points on it. Three different patterns of integer points satisfying the cone under consideration are obtained. A few interesting relations between the solutions and special number patterns namely Polygonal number, Pyramidal number, Centered Polygonal number, Centered Pyramidal number, pronic number and Star number are presented.

Keywords

Ternary homogeneous quadratic, integral solutions