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

On the Non Homogeneous Binary Quadratic Equation 4x2 – 3y2 = 37

  • Author:
  • S. Vidhyalakshmi1, E. Premalatha2,, D. Maheshwari3
  • Total Page Count: 5
  • Published Online: Jun 1, 2019
  • Page Number: 324 to 328

1Professor, Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamil Nadu620002, India

2Assistant Prolessor, Department of Mathematics, National College, Trichy, Tamil Nadu620001, India

3Assistant Professor, Department of Mathematics, Shrimati Indira Gandhi College, TrichyTamil Nadu620002, India

*Corresponding Author: E. Premalatha, Assistant Professor, Department of Mathematics, National College, Trichy, Tamil Nadu 620001, India. E-mail:premalathaem@gmail.com

Abstract

This paper deals with the problem of obtaining non-zero distinct integer solutions to the non homogeneous binary quadratic equation represented by the Pell-like equation 4x2 – 3y2 = 37. Different sets of integer solutions are presented. Employing the solutions of the above equation, integer solutions for other choices of hyperbolas and parabolas are obtained. A special Pythagorean triangle is also determined.

Keywords

Non homogeneous, binary quadratic, Pell-like equation, hyperbola, parabola, integral solutions, Special numbers, 11D09