Abstract
Consider a homogeneous additive polynomial of the form F(x)=a1x1k+a2x2k+⋯+asxsk, where the coefficients are integers. The function Γ⁎(k) is defined as the smallest number s of variables such that F is guaranteed to have a nontrivial zero in every p-adic field Qp regardless of the coefficients. In this article, we calculate the value of Γ⁎(k) for all 33≤k≤64 for which this value is not already known.
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