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On Non - Homogeneous Bi-Quadratic Diophantine Equation

Author(s):

Dr. P. Jayakumar , 1Professor of Mathematics, Annai Vailankanni Arts and Science College Thanjavur-613 007, T.N, India; R. Venkatraraman, Assistant Professor of Mathematics, SRM University Vadapalani Campus, Chennai -600026. Tamil Nadu,India

Keywords:

Quadratic, Non-Homogenous, Integer Solutions, Special Numbers, Polygonal, Pyramidal Numbers, 2010 Mathematics Subject Classification: 11D09

Abstract

Five different methods of the non-zero integral solutions of the homogeneous biquadratic Diophantine equation with five unknowns 8(x2 + y2) - 15xy = 40z4 are determined. Introducing the linear transformations x = u + v, y = u – v, u v 0 in 8(x2 + y2) -15xy = 40z4, it reduces to u2 +27v2 = 31z4. We are solved the above equation through various choices and are obtained the different methods of solutions which are satisfied it. Some interesting relations among the special numbers and the solutions are exposed.

Other Details

Paper ID: IJSRDV4I90113
Published in: Volume : 4, Issue : 9
Publication Date: 01/12/2016
Page(s): 181-183

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