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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 14 | Number 1 | Year 2014 | Article Id. IJMTT-V14P508 | DOI : https://doi.org/10.14445/22315373/IJMTT-V14P508

On The Quintic Equation with Three Unknowns


S.Vidhyalakshmi , A.Kavitha , M.A.Gopalan
Abstract

We obtain infinitely many non-zero integer triples (x,y,z) satisfying the quintic equation a(x2_y2)-(2a-1)xy=(k2+(4a-1)s2)nz5. A few interesting relations between the solutions and special numbers are presented.

Keywords
Quintic equation with three unknowns, integral solutions.
References

[1] L. E. Dickson, History of Theory of Numbers, Vol. 11, Chelsea Publishing Company, New York (1952).
[2] L. J. Mordell, Diophantine equations, Academic Press, London(1969).
[3] Carmichael , R. D. , The theory of numbers and Diophantine Analysis, Dover Publications, New York (1959)
[4] M. A. Gopalan & A. Vijayashankar, An Interesting Dio. problem , Advances in Mathematics, Scientific Developments and Engineering Application, Narosa Publishing House, 2010, Pg.1-6.
[5] M. A. Gopalan and G. Sangeetha, Integral solutions of ternary quintic Diophantine Equation , Bulletin of Pure and Applied Sciences, Vol29E(No. 1), 2010, 23-28.
[6] S. Vidhyalakshmi, K. Lakshmi and M. A. Gopalan, Integral solutions of the non-homogeneous ternary quintic equation , International Journal of Computational Engineering Research, Vol. 3, issues 4, 2013, 45-50.
[7] M. A. Gopalan & A. Vijayashankar, Integrated solutions of ternary quintic Diophantine equation , International Journal of Mathematical Sciences 19(1-2), (jan-june 2010), 165-169.
[8] S. Vidhyalakshmi, K. Lakshmi and M. A. Gopalan, Integral solutions of the non-homogeneous ternary quintic equation Archimedes Journal of Mathemctics, 3(2), 2013,197-204.

Citation :

S.Vidhyalakshmi , A.Kavitha , M.A.Gopalan, "On The Quintic Equation with Three Unknowns," International Journal of Mathematics Trends and Technology (IJMTT), vol. 14, no. 1, pp. 55-58, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V14P508

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