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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Waring's problem for twenty-two biquadrates


Author: Henry E. Thomas
Journal: Trans. Amer. Math. Soc. 193 (1974), 427-430
MSC: Primary 10J10; Secondary 10J05
DOI: https://doi.org/10.1090/S0002-9947-1974-0342478-7
MathSciNet review: 0342478
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Abstract | References | Similar Articles | Additional Information

Abstract: That every natural number is the sum of at most twenty-two biquadrates is proven by ascent from machine results on sums of six fourth powers.


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

  • [1] Emily M. Chandler, Waring's theorem for fourth powers, Dissertation, University of Chicago, Chicago, Ill., 1933.
  • [2] L. E. Dickson, Simpler proofs of Waring's theorem on cubes with generalizations, Trans. Amer. Math. Soc. 30 (1928).
  • [3] François Dress, Sur le problème de Waring pour les puissances quatrièmes, C. R. Acad. Sci. Paris Sér. A-B 272 (1971), A457–A459 (French). MR 0304311
  • [4] Henry E. Thomas, Jr., A numerical approach to Waring's problem for fourth powers, Dissertation, University of Michigan, Ann Arbor, Mich., 1973.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0342478-7
Keywords: Waring's problem, twenty-two biquadrates, ascent methods, sums of six fourth powers
Article copyright: © Copyright 1974 American Mathematical Society