
joint with C.L. Basile
We give an alternative proof of a theorem of R. HeathBrown regarding the existence of nonzero integral solutions of the equation p_{1} X_{1}^{3} + p_{2} X_{2}^{3} + p_{3} X_{3}^{3} + p_{4} X_{4}^{3} = 0, where the p_{j} are prime integers = 2 (mod 3).