2-Adic zeros of diagonal forms

Consider an additive form F(x)=a1x1d+a2x2d+⋯+asxsd whose coefficients are 2-adic integers. In this article we give an exact formula, in terms of d, for the smallest number of variables which guarantees that F has a nontrivial zero in the 2-adic integers regardless of the values of the coefficients.