International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
Call for Papers | Fully Refereed | Open Access | Double Blind Peer Reviewed

ISSN: 2319-7064


Downloads: 136 | Views: 224

Research Paper | Mathematics | India | Volume 5 Issue 11, November 2016


On Non- Homogeneous Biquadratic Diophantine Equation 7(x2+y2) - 13xy = 31z4

Dr. P. Jayakumar [14] | R. Venkatraman [6]


Abstract: Five different methods of the non-zero integral solutions of the homogeneous biquadratic Diophantine equation with five unknowns 7 (x2 + y2) - 13xy = 31z4 are determined. Introducing the linear transformations x = u + v, y = u v, u v 0 in 7 (x2 + y2) - 13xy = 31z4, it reduces to u2 +27v2 = 31z4. 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: Quadratic, non-homogenous, integer solutions, special numbers, polygonal, and pyramidal numbers


Edition: Volume 5 Issue 11, November 2016,


Pages: 391 - 394


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