LATTICE POINTS ON THE HOMOGENEOUS CONE: 5(X2+Y2) -9XY=23Z2

P.Jayakumar, V.Pandian, A.Nirmala

Abstract: Seven different method s of the non-zero non-negative solutions of homogeneous Diophantine equation 5(x2 + y2 ) – 9xy = 23z2 are obtained. Introducing the linear transformation x =u + v, y= u – v, u ??v??0 in 5(x2+y2 ) -9xy = 23z2 , it reduces to u 2 + 19v2 =23z2 . We are solved the above equation through various choices and are obtained seven different methods of solutions which are satisfied it. Some interesting relations among the special numbers and the solutions are exposed.

Keywords: The Method of Factorization, Integer Solutions, Linear Transformation, Relations and Special Numbers

DOI: https://doi.org/10.15623/ijret.2016.0508014