On The Non Homogeneous Heptic Equation with Five Unknowns
Journal: International Journal of Science and Research (IJSR) (Vol.3, No. 11)Publication Date: 2014-11-05
Authors : P. Jayakumar; K. Sangeetha;
Page : 3156-3162
Keywords : The non homogeneous Diophantine equation; Heptic equation with five unknowns; integral solutions; special numbers; a few interesting relation;
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.
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