LATTICE POINTS ON THE HOMOGENEOUS CUBIC EQUATION WITH FOUR UNKNOWNS x2 - xy + y2 + 4w2 = 8z3 - Somanath, Manju; Das, Radhika; Bindu, V.A (International Journal of Research -GRANTHAALAYAH, 2020)
The Homogeneous cubic equation with four unknowns represented by the equation x2 - xy + y2 + 4w2 = 8z3 is analyzed for its patterns of non zero distinct integral solutions. Here we exhibit four different patterns. In each pattern we can find some interesting relations between the solutions and special numbers like Polygonal number, Three-Dimensional Figurate number, Star number, Rhombic Dodecahedral number etc.