Paper Title

A Ternary Quadratic Diophantine Equation 39x^ 2-72xy+ 39y^ 2= 246z^ 2

Authors

Gnanendra Rao

Keywords

Homogeneous Quadratic
TernaryQuadratic
Integer solutions
polygonal number andpyramidal number

Article Type

Original Article

Journal

Journal:International Research Journal of Engineering and Technology (IRJET)

Issue

Volume : 5 | Issue : 4 | Page No : 3041-3044

Published On

April, 2018

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Abstract

The Homogeneous Ternary Quadratic Diophantine Equation is given by and analyzed for its patterns of non-zero distinct integer solutions. A few interesting relations among the solutions and special polygonal, pyramidal, Mersenne, Carol and Gnomonic, and Pronic numbers are presented. Introducing the linear transformation x=u+v, y=u-v, and employing the method of factorization, different patterns of non-zero distinct integer solutions to the equation in the title are obtained.