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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. : 245-252, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2019.00023.7 (Received on 07.01.2019 Revised on 20.04.2019 Accepted on 08.05.2019)

ON THE HOMOGENEOUS CONE $3{x^2} - 8{y^2} = 25{z^2}$

M.A. Gopalan1, Sharadha Kumar2,*
Author’s Affiliation : 1Professor, Department of Mathematics, SIGC, Trichy, Tamil Nadu 620002, India. E-mail: [email protected] 2M.Phil Scholar, Department of Mathematics, SIGC, Trichy, Tamil Nadu 620002, India. E-mail: [email protected]

Corresponding Author : Sharadha Kumar, M.Phil Scholar, Department of Mathematics, SIGC, Trichy, Tamil Nadu 620002, India.,
E-Mail:-[email protected]


Abstract

This paper aims at determining non-zero distinct integer solutions satisfying the homogeneous cone represented by the ternary quadratic equation $3{x^2} - 8{y^2} = 25{z^2}$. 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.

2010 A.M.S. Mathematics Subject Classification: 11D09.

Keywords

Ternary quadratic, homogeneous quadratic, homogeneous cone, integer solutions
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