Integral Solutions of the Octic Equation With Five Unknowns $(x-y)(x^{3}+y^{3})=4(w^{2}-p^{2})T^{6}$


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Authors

  • S. Vidhyalakshmi Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamilnadu, India
  • A. Kavitha Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamilnadu, India
  • M. A. Gopalan Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamilnadu, India

Keywords:

Octic non-homogeneous equation, Pyramidal numbers, Pronic numbers, Fourth, fifth and sixth dimensional figurate numbers

Abstract

The non-homogeneous octic equation with five unknowns represented by the Diophantine equation $(x-y)(x^{3}+y^{3})=4(w^{2}-p^{2})T^{6}$ is analyzed for its patterns of non-zero distinct integral solutions and seven different patterns of integral solutions are illustrated. Various interesting relations between the solutions and special numbers, namely, Pyramidal numbers, Pronic numbers, Stella octangular numbers, Gnomonic numbers, polygonal numbers, four dimensional figurate numbers are exhibited.

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Published

01-12-2015

How to Cite

S. Vidhyalakshmi, A. Kavitha, & M. A. Gopalan. (2015). Integral Solutions of the Octic Equation With Five Unknowns $(x-y)(x^{3}+y^{3})=4(w^{2}-p^{2})T^{6}$. International Journal of Mathematics And Its Applications, 3(4 - A), 1–7. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/480

Issue

Vol. 3 No. 4 - A (2015)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.