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