Lattice Points on the Homogeneous Cone 4(X2+Y2) ? 3XY =19Z2

Dr. P. Jayakumar ^[14] | G. Shankarakalidoss ^[2]

Abstract: The ternary quadratic homogeneous equation given by 4 (X2 + Y2) 3XY = 19Z2 is analyzed for its non-zero distinct integer points. Six different patterns of integer points satisfying under consideration are obtained. A few interesting relation between the solutions and special number patterns namely Polygonal number, Pyramidal number and Nasty number are presented.

Keywords: Ternary homogeneous quadratic, integral solutions, special number

Edition: Volume 4 Issue 1, January 2015,

Pages: 2053 - 2055

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Lattice Points on the Homogeneous Cone 4(X2+Y2) ? 3XY =19Z2

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