On Non- Homogeneous Biquadratic Diophantine Equation 7(x2+y2) - 13xy = 31z4
Journal: International Journal of Science and Research (IJSR) (Vol.5, No. 11)Publication Date: 2016-11-05
Authors : P. Jayakumar; R. Venkatraman;
Page : 391-394
Keywords : Quadratic; non-homogenous; integer solutions; special numbers; polygonal; and pyramidal numbers;
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
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