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

Dr. P. Jayakumar, R. Venkatraman

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

How to Cite?: Dr. P. Jayakumar, R. Venkatraman, "On Non- Homogeneous Biquadratic Diophantine Equation 7(x2+y2) - 13xy = 31z4", Volume 5 Issue 11, November 2016, International Journal of Science and Research (IJSR), Pages: 391-394, https://www.ijsr.net/getabstract.php?paperid=ART20162748, DOI: https://dx.doi.org/10.21275/ART20162748