Non-Homogeneous Cubic Equation with Three Unknowns

The non-homogeneous cubic equation with three unknowns represented by 2 2 3 3(x ? y ) ? 5xy ? 2(x ? y) ? 4 ? 27z is analyzed for finding its non-zero distinct integral solutions. Three different methods have been presented for determining the integral solutions of the non-homogeneous cubic equation under consideration. Employing the integral solutions of the above equation, a few interesting relations between special numbers are exhibited. The non-homogeneous cubic equation with three unknowns represented by 2 2 3 3(x ? y ) ? 5xy ? 2(x ? y) ? 4 ? 27z is analyzed for finding its non-zero distinct integral solutions. Three different methods have been presented for determining the integral solutions of the non-homogeneous cubic equation under consideration. Employing the integral solutions of the above equation, a few interesting relations between special numbers are exhibited.