On Non-Homogeneous Bi-Quadratic Diophantine Equation 4(x2+y2)-7xy = 19z4

Dr. P. Jayakumar, V. Pandian, R. Venkatraman

Abstract: Five different methods of the non-zero integral solutions of the homogeneous biquadratic Diophantine equation with five unknowns 4 (x2 + y2) -7xy =19z4 are determined. Some interesting relations among the special numbers and the solutions are exposed

Keywords: Quadratic, non-homogenous, integer solutions, special numbers, polygonal, and pyramidal numbers