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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2019, Volume & Issue : BPAS-Maths & Stat 38E(1), JAN-JUN 2019
Page No. : 324-328, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2019.00033.X (Received on 10.01.2019 Revised on 01.05.2019 Accepted on 30.05.2019)

ON THE NON HOMOGENEOUS BINARY QUADRATIC EQUATION $4{x^2} - 3{y^2} = 37$

S. Vidhyalakshmi1, E. Premalatha2,*, D. Maheshwari3
Author’s Affiliation : 1Professor, Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamil Nadu 620002, India. 2Assistant Professor, Department of Mathematics, National College, Trichy, Tamil Nadu 620001, India. 3Assistant Professor, Department of Mathematics, Shrimati Indira Gandhi College, Trichy Tamil Nadu 620002, India.

Corresponding Author : E. Premalatha, Assistant Professor, Department of Mathematics, National College, Trichy, Tamil Nadu 620001, India.,
E-Mail:-[email protected]


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 $4{x^2} - 3{y^2} = 37$. 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.

2010 Mathematics Subject Classification: 11D09.

Keywords

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