Research Paper | Mathematics | India | Volume 3 Issue 11, November 2014

On The Non Homogeneous Heptic Equation with Five Unknowns ?(x?^2-y^2)(9x^2+9y^2-16xy)=21(X^2-Y^2)z^5

P. Jayakumar, K. Sangeetha

The non homogeneous Diophantine equation of degree seven with five unknowns represented by (x^2-y^2) (9x^2+9y^2-16xy) =21 (X^2-Y^2) z^5 is analyzed for its non - zero distinct integer solutions. Employing suitable linear transformations and applying the method of cross multiplication, four different patterns of non-zero distinct integer solutions to the heptic equation under consideration are obtained. A few interesting relation between the solutions and special numbers namely Polygonal numbers, Pyramidal numbers, Centered Pyramidal numbers, Star numbers and Stella octangular numbers are exhibited.

**Keywords:** The non homogeneous Diophantine equation, Heptic equation with five unknowns, integral solutions, special numbers, a few interesting relation,

**Edition:** Volume 3 Issue 11, November 2014

**Pages:** 3156 - 3162

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How to Cite this Article?

P. Jayakumar, K. Sangeetha, "On The Non Homogeneous Heptic Equation with Five Unknowns ?(x?^2-y^2)(9x^2+9y^2-16xy)=21(X^2-Y^2)z^5", International Journal of Science and Research (IJSR), https://www.ijsr.net/search_index_results_paperid.php?id=SUB14122, Volume 3 Issue 11, November 2014, 3156 - 3162

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