K. Thangamalar


The ternary quadratic equation in place of non-homogeneous cone given by  is analyzed for its non-zero discrete integer points on it. The different patterns of integer points fulfilling the cone under consideration are obtained. A few interesting dealings between the solutions and special number patterns are offered

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L.E Dickson, History of theory of Numbers, Vol.2, Chelsea publishing company, New York 1952.

M.A. Gopalan, D. Geetha, Lattice points on the hyperbolic of two sheets x^2-6xy+y^2+6x-2y+5=z^2+4, impact J. sci tech; Vol (4), No.1, 23-32, 2010.

M.A. Gopalan, and V. Pandichelvi, Integral solutions of ternary quadratic equation z(x-y)=4xy, Impact J.sci TSech; Vol(5), No.1, 01-06-2011.

M.A. Gopalan, S. Vidhyalakshmi and A. Kavitha, Integral points on the homogenous Cone z^2=2x^2-7y^2, Diophantus J.Math., 1(2), 109-115, 2012.

M.A. Gopalan, J. Kalinga Rani, on ternary quadratic equation x^2+y^2=z^2+8, impact J.sci tech; Vol(5), No. 1, 39-43, 2011.

M.A. Gopalan, S. Vidhyalakshmi and G. Sumathi, Lattice points on the hyperboloid one sheet 〖4z〗^2=2x^2-7y^2, Diophantus J.math, 1(2), 109-115,2012.

M.A.Gopalan, S. Vidhyalakshmi and K. Lakshmi, Integral points on the hyperboloid for two sheets 〖3y〗^2=7x^2-z^2+21, Diophantus J.math, 1(2), 99-107, 2012.

M.A. Gopalan and G. Sangeetha, Observation on y^2=3x^2-2z^2, Antarctica, J.math, 9(4), 359-362, 2012.

M.A. Gopalan and G. Srividhya, Observation on y^2=3x^2-2z^2, Archimedes J.math, 2(1), 7-15, 2012.

M.A. Gopalan, and S. Vidhyalakshmi, on the ternary quadratic equation x^2=(a^2-1)(y^2-z^2 ),∝>1, Bessel J.math., 2(2), 147-151, 2012.

Manju Somanath, G. Sangeetha, and M.A. Gopalan, Observations on the ternary Quadratic equation y^2=3x^2+z^2, Bessel J.math., 2(2),101-105,2012.

G. Akila, M.A. Gopalan and S. Vidhyalakshmi, Integral solution of 43x^2+y^2=z^2, IJOER, Vol.1, Issue 4, 70-74, 2013.

T.Nancy, M.A. Gopalan, and S. Vidhyalakshmi, on Ternary Deiophantine equation 47X^2+Y^2=Z^2, IJOER, Vol. I, Issue 4, 51-55, 2013.

Anbuselvi R, Kannaki K, On ternary Quadratic Equation 11x^2+〖3y〗^2=14z^2 Volume 5, Issue 2, Feb 2016, Pg No. 65-68.

Anbuselvi R, Kannaki K, On ternary Quadratic Equation x^2+〖xy+y〗^2=12z^2 IJAR 2016: 2 (3); 533-535.

Thangamalar K, On the ternary cubic diophantine equation 5x^2-2y^2=3z^2, IJREAM December 2018, Volume - 4, Issue – 6, ISSN No. 2454-9150, Impact Factor 5.646.


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