Vaserstein, L. N. Sums of cubes in polynomial rings. (English) Zbl 0711.11013 Math. Comput. 56, No. 193, 349-357 (1991). By studying sums of cubes in the ring F[x] of polynomials over a field F of characteristic \(\neq 3\) and with cardinality \(\neq 2\), 4, the author proves the nice result that for any associative ring A with a 1 and of prime characteristic \(\neq 0,2,3\), every element in A is a sum of 3 cubes in A. The proof, which is by consideration of cases, took a great deal of computing time in searching for solutions and, in contrast with the result, is long and involved. Reviewer: M.Dodson Cited in 9 Documents MSC: 11C08 Polynomials in number theory 11P05 Waring’s problem and variants 16U99 Conditions on elements Keywords:polynomial rings; sums of cubes PDFBibTeX XMLCite \textit{L. N. Vaserstein}, Math. Comput. 56, No. 193, 349--357 (1991; Zbl 0711.11013) Full Text: DOI