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Proceedings of the American Mathematical Society

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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
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] P. Erdös and M. B. Nathanson, Lagrange's theorem and thin subsequences of squares, Contributions to Probability: A Collection of Papers Dedicated to Eugene Lukacs, (J. Gani and V. K. Rohatgi, eds.), Academic Press, New York (to appear). MR 618672 (82f:60005)
  • [2] E. Härtter and J. Zöllner, Darstellungen natürlichen Zahlen als Summe und als Differenz von Quadraten, Norske Vidensk. Selsk. Skr. (Trondheim) 1 (1977), 1-8. MR 0506101 (58:21984)

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Keywords: Sums of squares, Lagrange's theorem, addition of sequences
Article copyright: © Copyright 1980 American Mathematical Society

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