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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 58 | Number 1 | Year 2018 | Article Id. IJMTT-V58P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V58P504

Generation Formula for Integer Solutions to Special Elliptic Paraboloids


S.Vidhyalakshmi, M.A.Gopalan, S. Aarthy Thangam
Abstract

Knowing a solution of ternary quadratic diophantine equation representing elliptic paraboloid, a general formula for generating sequence of solutions based on the given solution is illustrated.

Keywords
ternary quadratic, generation of solutions, elliptic paraboloid.
References

[1] M.A. Gopalan, S. Vidhyalakshmi, N. Thiruniraiselvi, “Observations on x^2 + y^2 = 17z^2 ”, Diophantus J.Math , 1(2), 77-83, 2012.
[2] S. Divya, M.A. Gopalan, S. Vidhyalakshmi, “Lattice points on the homogeneous cone x^2 + y^2 = 40z^2 ”, The Experiment, 17(3), 1191-1199, 2013.
[3] M.A. Gopalan, S. Vidhyalakshmi, E. Premalatha, “On the homogeneous quadratic equation with 3 unknowns x^2-xy+y2 =( k^2+3)z^2 ”, Bull.Math.of Stat. Res., 1(1), 38-41, 2013.
[4] Gopalan et al, “Integer points on the homogeneous cone 2x^2 + 3y^2 = 35x^2 ”, Indian journal of Science, 7(17), 6-10, 2014.
[5] K. Geetha, Manju Somnath, M.A. Gopalan, “A ternary quadratic diophantine equation x^2 + y^2 = 10z^2 ”, IJETER, 4(1), 96-99, January 2016.
[6] V. Geetha, M.A. Gopalan, “Observations on 2 x^2 + y^2 = 2(k^2 + 1 )z^2 ”, Transactions on Mathematics, 2(3), 37-43, July 2016.
[7] M.A. Gopalan, S. Vidhyalakshmi, Presenna Ramanand, “Generation formula for solutions to ternary quadratic diophantine equation”, International Journal of Advanced Research and Development, 3(3), 78-79, May 2018.

Citation :

S.Vidhyalakshmi, M.A.Gopalan, S. Aarthy Thangam, "Generation Formula for Integer Solutions to Special Elliptic Paraboloids," International Journal of Mathematics Trends and Technology (IJMTT), vol. 58, no. 1, pp. 20-23, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V58P504

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