Intrinsic Solution on Quadratic Diophantine Equation

Abstract

The non-zero unique integer solutions of the Quadratic Diophantine Equation with three unknowns are examined. There are several absorbing relationships between the answers and a few unique numbers of rank n that arespecial Polygonal numbers, Star number and Gnomonic numbers.

Introduction

Conclusion

The Diophantine quadratic equation using special polygonal numbers has been presented. Futhermore, one can look for integer solutions of the quadratic diophantine equations with other special numbers.

References

[1] Batta.B and Singh.A.N, History of Hindu Mathematics, Asia Publishing House 1938. [2] Carmichael, R.D., “The Theory of Numbers and Diophantine Analysis”, Dover Publications, New York, 1959. [3] Dickson,.L.E., “History of the theory of numbers”, Chelsia Publishing Co., Vol.II, New York, 1952. [4] Mollin.R.A., “All solutions of the Diophantine equation ,”, For East J.Math.Sci., Social Volume,1998, Part III, page-257-293. [5] Mordell.L.J., “Diophantine Equations”, Academic Press, London 1969. [6] Telang.S.G., “Number Theory”, Tata McGraw-Hill Publishing Company, New Delhi 1996. [7] Nigel.P.Smart,”The Algorithmic Resolutions of Diophantine Eqautions”, Cambridege University Press, London 1999. [8] Gopalan.M.A., Manju Somanath, and Vanitha.N., “Integral Solutions of ”, ActaCienciaIndica, Volume 33;number 4, pages 1287-1290, 2007. [9] Gopalan.M.A., and Anbuselvi.R., “A special Pythagorean triangle”, Acta Ciencia Indica, Volume 31, number 1, pages 53-54, 2005. [10] Gopalan.M.A., and Devibala.S., “A special Pythagorean triangle”, Acta Ciencia Indica, Volume 31, number 1, pages 39-40, 2005. [11] Gopalan.M.A., and Anbuselvi.R, “On Ternary Quadratic Homogeneous Diophantine Equation ”, Bulletin of Pure and Applied Science, Vol.25E, No.2, Pp.405-408, 2005. [12] Gopalan.M.A., Vidyalakshmi.S and Devibala.S “Integral Solutions of ”, Bulletin of Pure and Applied Science, Vol.25E, No.2, Pp.401-406, 2006. [13] Gopalan.M.A., and Devibala.S., “OnTernary Quadratic Homogeneous Equation , Bulletin of Pure and Applied Science, Vol.24E, No.1, Pp.25-28, 2005. [14] Janaki.G., and Vidhya.S., “Observations on Ternary Quadratic Diophantine Equation ”, International Research Journal of Engineering and Technology, Vol.04, No.3, Pp.1239-1245, 2017.

Copyright

Copyright © 2024 S. Vidhya, S. Sivaranjani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.