Observation on the Ternary Quadratic Diophantine Equation x2 = 22k+1 (3z2 – y2 )

G  Sangeetha; B  Rena Caroline and C  Shirley Shalini

doi:10.17485/ijst/2016/v9i1/85775

Article

Observation on the Ternary Quadratic Diophantine Equation x2 = 22k+1 (3z2 – y2 )

VIEWS 926
PDF 278

Abstract
Full-Text HTML
Full-Text PDF
How to Cite

Indian Journal of Science and Technology

DOI: 10.17485/ijst/2016/v9i1/85775

Year: 2016, Volume: 9, Issue: 1, Pages: 1-3

Original Article

Observation on the Ternary Quadratic Diophantine Equation x2 = 22k+1 (3z2 – y2 )

G. Sangeetha^* , B. Rena Caroline and C. Shirley Shalini

Department of Mathematics, Vel Tech Multitech, Chennai - 600062, Tamil Nadu, India; [email protected], [email protected], [email protected]

*Author For Correspondence
G. Sangeetha
Department of Mathematics, Vel Tech Multitech, Chennai - 600062, Tamil Nadu, India; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: Finding the integral solutions of ternary quadratic equation and the relation between parameters/solutions. The ternary quadratic Diophantine equation is studied for it’s non-trivial distinct integral solutions. Findings: Employing the integral solutions of the equation under consideration infinitely many Pythagorean triangles are obtained where each of which satisfies the relation “Hypotenuse-4(area/Perimeter) is a Nasty number”.

Keywords: Integral Solutions, Ternary Quadratic Equation