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Mathematics of Computation

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Sums of cubes in polynomial rings

Author: L. N. Vaserstein
Journal: Math. Comp. 56 (1991), 349-357
MSC: Primary 11P05; Secondary 11C08
MathSciNet review: 1052104
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Abstract: For any associative ring A with 1 of prime characteristic $ \ne 0,2,3$, every element of A is the sum of three cubes in A.

References [Enhancements On Off] (What's this?)

  • [1] K. Mahler, Note on hypothesis K of Hardy and Littlewood, J. London Math. Soc. 11 (1936), 136-138.
  • [2] L. J. Mordell, On the representation of an integer as the sum of four integer cubes, Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969) Academic Press, London, 1971, pp. 115–117. MR 0321855
  • [3] R. E. A. C. Paley, Theorems on polynomials in a Galois field, Quart. J. Math. 4 (1933), 52-63.
  • [4] L. N. Vaserstein, Waring’s problem for algebras over fields, J. Number Theory 26 (1987), no. 3, 286–298. MR 901241, 10.1016/0022-314X(87)90085-0

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Article copyright: © Copyright 1991 American Mathematical Society