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1105: First Steps in a Mysterious Quest

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The Mathematics of Paul Erdős I
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Abstract

During the summer of 1975, I spent a few days with my mother and sister who were on holidays near La Baule. I had just left École Polytechnique, and needed some rest after the military service.

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Notes

  1. 1.

    Balasubramanian, Deshouillers and Dress established in 1986 that g(4) = 19, thereby closing up (in a certain sense, which would take us too far to describe here) Waring’s classical problem.

  2. 2.

    See our book Divisors for an expository text on this subject.

  3. 3.

    But this density is strictly positive, which shows that the tendency on which Erdős based his conjecture is nevertheless quite constraining.

References

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  2. R. Balasubramanian, J.-M. Deshouillers & F. Dress, Problème de Waring pour les bicarrés, 2 : résultats auxilaires pour le théorème asymptotique, C.R. Acad. Sci. Paris 303 (1986), 161–163.

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  3. P. Erdős, On an asymptotic inequality in the theory of numbers (Russian), Vestnik Leningrad Univ. 13 (1960), 41–49.

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Correspondence to Gérald Tenenbaum .

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Tenenbaum, G. (2013). 1105: First Steps in a Mysterious Quest. In: Graham, R., Nešetřil, J., Butler, S. (eds) The Mathematics of Paul Erdős I. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7258-2_20

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