ON THE NON HOMOGENEOUS HEPTIC DIOPHANTINE EQUATION (X2- Y2)(8X2 + 8Y2 -14XY) = 19 (X2 –Y2) Z5

P.Jayakumar, V.Pandian, J.Meena

Abstract: Five different methods of the non-zero non-negative solutions of non- homogeneous Heptic Diophantine equation (x2 - y 2 )(8x 2 + 8y 2 -14xy) = 19(X2 –Y 2 ) z5 are observed. . Introducing the linear transformations x = u + v, y = u – v, X= 2u + v, Y= 2u –v, u ? v ? 0 in (x2 - y 2 ) (8x2 + 8y2 -14xy) = 19 (X2 –Y 2 ) z5 , it reduces to u 2 +15v2 = 19z5 . We are solved the above equation through various choices and the different methods of solutions which are satisfied it. Some interesting relations among the special numbers and the solutions are exposed

Keywords: The Diophantine Equation, Heptic Equation, Integral Solutions, Special Numbers, A Few Interesting Relation

DOI: https://doi.org/10.15623/ijret.2016.0504033