Volume 38 | Number 2 | Year 2016 | Article Id. IJMTT-V38P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V38P516
The ternary homogeneous equation representing an infinite cone given by is analyzed for its non-zero distinct integer points. Few different patterns of integer points satisfying the infinite cone under consideration are obtained.
[1] Ivan Niven, Herbert S. Zuckermann and Hugh L. Montgomery, an introduction to the Theory of Numbers, John Wiley & Sons Inc, New York, 2004.
[2] Andre weil, Number Theory : An Approach through History, From Hammurapito to Legendre, Bikahsuser, Boston, 1987.
[3] Bibhotibhusan Batta and Avadhesh Narayanan Singh, History of Hindu Mathematics, Asia Publishing House, 1983.
[4] Boyer. C. B., History of mathematics, John Wiley & sons lnc., New York, 1968.
[5] L.E. Dickson, History of Theory of Numbers, Vol.2, Chelsea Publishing Company, New York, 1952.
[6] Davenport, Harold (1999), The higher Arithmetic: An introduction to the Theory of Numbers (7th ed.) Cambridge University Press.
[7] John Stilwell, Mathematics and its History, Springer Verlag, New York, 2004.
[8] James Matteson, M.D. “A Collection of Diophantine problems with solutions” Washington, Artemas Martin, 1888.
[9] Tituandreescu, DorinAndrica, “An introduction to Diophantine equations” Springer Publishing House, 2002.
[10] Conway J H and Guy R K, The book of numbers, Springer Science and Business Media, 2006.
[11] Manju Somanath, J. Kannan, K.Raja, “Lattice Points of an infinite cone International Journal of Recent Innovation Engineering and Research Vol. 1, Issue 5, Pp.14-16, September 2016.
[12] M. A .Gopalan, Manju Somanath, K.Geetha, On Ternary Quadratic Diophantine Equation ,International Journal for research in emerging Science and technology, Vol.3, Issue3, Pp.644-648,February2016.
[13] M. A .Gopalan, Manju Somanath, K.Geetha, On Ternary Quadratic Diophantine Equation Bulletin of Mathematics and Statistics research,Vol.2,issue1,Pp.1-8,2014.
[14] Manju Somanath, Sangeetha G, Gopalan M. A On the ternary quadratic equation , IJIRSET, Vol.2 No.6,pp.2008-2010. June 2013.
[15] Manju Somanath, Sangeetha G, Gopalan M. A., Relations among special figurate numbers through equation , impact J, Sci. Tech. Vol.5,No.1,pp.57-60, 2011.
[16] Gopalan M.A., Sangeetha V and Manju Somanath, Observations on the ternary quadratic equation , Bulletin of Society for Mathematical Services & Standards, Vol. 3, No. 2, pp.88-91, 2014.
[17] Gopalan M. A., and Palanikumar R, Observations on , Antarctica J. Math. Vol.8,No.2, pp.149- 152,2011.
[18] Gopalan M. A., Vidhyalakshmi S., Sumathi G., Lattice points on the elliptic paraboloid , Advances in Theoretical and Applied Mathematics, Vol.7 .No.43, pp.79-85,2012.
[19] Integral points on the homogeneous cone , Discovery Science, Vol.3, No.7 pp.5-8, Jan.2013.
Manju Somanath, J. Kannan, K. Raja, "Lattice Points of an Infinite Cone x2+y2=(α2n+ß2n)z2," International Journal of Mathematics Trends and Technology (IJMTT), vol. 38, no. 2, pp. 95-98, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V38P516