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Review of Information Engineering and Applications

December 2014, Volume 1, 2, pp 93-101

On Homogeneous Cubic Equation with Fourunknowns x3+y3= 2lzw2

M.A. Gopalan

,

S. Vidhyalakshmi

,

N. Thiruniraiselvi

M.A. Gopalan 1 ,

S. Vidhyalakshmi 1 N. Thiruniraiselvi 3

  1. Professor, Department of Mathematics, SIGC, Trichy, Tamilnadu, India 1

  2. Research Scholar, Department of Mathematics, SIGC, Trichy, Tamilnadu, India 3

Pages: 93-101

DOI: 10.18488/journal.79/2014.1.2/79.2.93.101

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Abstract:

The homogeneous cubic equation with four unknowns represented by the Diophantine    equation  x3+y3= 2lzw2   is analyzed for its patterns of non – zero distinct integer solutions. A few interesting properties between the solutions and special numbers, namely, Polygonal number, Pyramidal number, Centered polygonal number, Stella octangular number and Octahedral number    are presented. 
Contribution/ Originality
This study contributes in the existing literature different approaches of determining non-zero distinct integer solutions to the homogeneous equation of degree three with 4 unknowns given by x3+y3= 2lzw2

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Reference:

  1. L. E. Dickson, History of theory of numbers, diophantine analysis vol. 2. New York: Dover, 2005.
  2. L. J. Mordell, Diophantine equations. New York: Academic Press, 1969.
  3. R. D. Carmichael, The theory of numbers and diophantine analysis. New York: Dover, 1959.
  4. M. A. Gopalan, S. Manju, and N. Vanitha, "On ternary cubic diophantine equation  ," Advances in Theoretica and Applied Mathematics, vol. 1, pp. 227-231, 2006.
  5. M. A. Gopalan, S. Manju, and N. Vanitha, "Ternary cubic diophantine equation  ," Acta Ciencia Indica, vol. 34M, pp. 1135-1137, 2008.
  6. M. A. Gopalan and G. Sangeetha, "On the ternary cubic diophantine equation ," Archimedeas Journal of Mathematics, vol. 1, pp. 7-14, 2011.
  7. M. A. Gopalan and S. Premalatha, "Integral solutions of  ," Bulletin of Pure and Applied Sciences, vol. 29E, pp. 197-202, 2009.
  8. M. A. Gopalan and V. Pandi Chelvi, "Remarkable solutions on the cubic equation with four unknows  ," Antarctica J. Math, vol. 4, pp. 393-401, 2010.
  9. M. A. Gopalan and B. Sivagami, "Integral solutions of homogeneous cubic equation with four unknows  ," Impact.J.Sci.Tech., vol. 4, pp. 53-60, 2010.
  10. M. A. Gopalan and S. Premalatha, "On the cubic diophantine equation with four unknows  ," International Journal of Mnathematical Sciences, vol. 9, pp. 171-175, 2010.
  11. M. A. Gopalan and J. Kaliga Rani, "Integral solutions of   ," Bulletin of Pure and Applied Sciences, vol. 29E, pp. 169-173, 2010.
  12. M. A. Gopalan and S. Premalatha, "Integral solutions of  ," The Global Journal of Applied Mathematics and Mathematical Sciences, vol. 3, pp. 51-55, 2010.
  13. M. A. Gopalan, S. Vidhyalakshmi, and S. Mallika, "Observation on the cubic equation with four unknows   " The Global Journal of Mathematics and Mathematical Sciences, vol. 2, pp. 69-74, 2012.
  14. M. A. Gopalan, S. Vidhyalakshmi, and S. Mallika, "Observation on the cubic equation with four unknows  ," IJAMP, vol. 4, pp. 103-107, 2012.
  15. M. A. Gopalan, S. Vidhyalakshmi, and G. Sumathi, "On the homogeneous cubic equation with four unknows  ," Discovery, vol. 2, pp. 17-19, 2012.
  16. M. A. Gopalan and K. Geetha, "Observation on the cubic equation with four unknows,  " International Journal of Pure and Applied Mathematics Sciences, vol. 6, pp. 25-30, 2013.
  17. M. A. Gopalan, S. Vidhyalaksmi, and N. Thiruniraiselvi, "On homogeneous cubic equation with four unknowns  ," Cayley J.Math., vol. 2, pp. 163-168, 2013.
  18. M. A. Gopalan, S. Vidhyalaksmi, and A. Kavitha, "Observations on the homogeneous cubic equation with four unknowns  ," Bessel J.Math., vol. 4, pp. 1-6, 2014.

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