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Research Paper | Mathematics | Volume 3 Issue 11, November 2014 | Pages: 3156 - 3162 | India
On The Non Homogeneous Heptic Equation with Five Unknowns
Abstract: 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,
How to Cite?: P. Jayakumar, K. Sangeetha, "On The Non Homogeneous Heptic Equation with Five Unknowns", Volume 3 Issue 11, November 2014, International Journal of Science and Research (IJSR), Pages: 3156-3162, https://www.ijsr.net/getabstract.php?paperid=SUB14122, DOI: https://dx.doi.org/10.21275/SUB14122