• R.Anbuselvi Associate Professor of Mathematics, ADM College for women (Autonomous), Nagapattinam, Tamilnadu, India
  • K.Kannaki Lecturer of Mathematics, Valivalam Desikar Polytechnic College, Nagapattinam, Tamilnadu, India


Ternary non-homogeneous quadratic, integral solutions


The ternary quadratic equation representing non-homogeneous cone given by  is analyzed for its non-zero distinct integer points on it. The different patterns of integer points satisfying the cone under consideration are obtained. A few interesting relations between the solutions and special number patterns are presented.


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.

Manju Somanath, G. Sangeetha and M.A. Gopalan, on the homogeneous ternary Quadratic Diophantine equation x^2+(2k+1) y^2=〖(k+1)〗^2 z^2, Bessel J.math, 2(2) 107-110, 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.

M.A. Gopalan, S. Vidhyalakshmi and C. Nithya, Integral points on the ternary Quadratic Diophantine equation 3x^2+〖5y〗^2=128z^2, Bull.Math., & Stat. Res Vol.2, Issue 1, 25-31, 2014.

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.

Anbuselvi R, Kannaki K, On ternary Quadratic Equation 〖3(x〗^2+y^2)-5xy+x+y+1=15z^3 IJSR Sep 2016: 5(9); 42-48.

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How to Cite

R.Anbuselvi, & K.Kannaki. (2017). ON TERNARY QUADRATIC DIOPHANTINE EQUATION. International Education and Research Journal (IERJ), 3(2). Retrieved from https://ierj.in/journal/index.php/ierj/article/view/667