ON NON- HOMOGENEOUS BIQUADRATIC DIOPHANTINE EQUATION 5(X2+Y2) -9XY = 23Z4

P.Jayakumar, V.Pandian

Abstract: Five different methods of the non-zero integral solutions of the homogeneous biquadratic Diophantine equation with five unknowns 5(x2 + y 2 ) - 9xy =23z 4 are determined. Introducing the linear transformations x = u + v, y = u – v, u ? v ? 0 in 5(x2 + y 2 ) - 9xy = 23z 4 , it reduces to u 2 +19v 2 = 23z4 . 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

DOI: https://doi.org/10.15623/ijret.2016.0504029