Abstract
Sufficient conditions for a cubic form ω in n variables to be representable as a sum of cubes of n + m [ m ⩽(n−2) 2 ] linear forms are derived. For m=0, 1 the conditions are also necessary (whether it is true for m >1 is an open question). In each case the corresponding algorithm requires, besides arithmetic operations over the coefficients of ω, solving one algebraic equation of degree m + n.
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