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On Homogeneous Diophantine Equation X^2 + Y^2 - XY = 7Z^2

Author(s):

Shankarakalidoss. G , KINGS COLLEGE OF ENGINEERING; Jeyakumar. P, ANNAI VELANKANNI COLLEGE OF ARTS AND SCIENCE

Keywords:

Ternary Homogeneous Quadratic, Integral Solutions

Abstract

The ternary quadratic homogeneous equation representing homogeneous cone given by X^2 + Y^2 - XY = 7Z^2 is analyzed for its non-zero distinct integer points on it. Six different patterns of and special number patterns namely Polygonal number, Pyramidal number, Octahedral number and Nasty number are presented. Also knowing and integer solution satisfying the given cone, two triplex of integers generated from the given solution are exhibited.

Other Details

Paper ID: IJSRDV5I90283
Published in: Volume : 5, Issue : 9
Publication Date: 01/12/2017
Page(s): 456-458

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