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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Lagrange's theorem with $ N\sp{1/3}$ squares


Authors: S. L. G. Choi, Paul Erdős and Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 79 (1980), 203-205
MSC: Primary 10J05
DOI: https://doi.org/10.1090/S0002-9939-1980-0565338-3
MathSciNet review: 565338
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Abstract: For every $ N > 1$ we construct a set A of squares such that $ \vert A\vert < (4/\log 2){N^{1/3}} \log N$ and every nonnegative integer $ n \leqslant N$ is a sum of four squares belonging to A.


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

  • [1] J. Gani and V. K. Rohatgi (eds.), Contributions to probability, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. A collection of papers dedicated to Eugene Lukacs. MR 618672
  • [2] Erich Härtter and Joachim Zöllner, Darstellungen natürlicher Zahlen als Summe und als Differenz von Quadraten, Norske Vid. Selsk. Skr. (Trondheim) 1 (1977), 8 (German, with English summary). MR 0506101

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0565338-3
Keywords: Sums of squares, Lagrange's theorem, addition of sequences
Article copyright: © Copyright 1980 American Mathematical Society