The Erdős-Moser equation 1k + 2k + ··· +(m-1)k revisited using continued fractions

Title: The Erdős-Moser equation 1k + 2k + ··· +(m-1)k revisited using continued fractions
Creator: Gallot, Yves; Moree, Pieter; Zudilin, W.
Relation: Mathematics of Computation Vol. 80, p. 1221-1237
Publisher Link: http://dx.doi.org/10.1090/S0025-5718-2010-02439-1
Publisher: American Mathematical Society
Resource Type: journal article
Date: 2011
Description: If the equation of the title has an integer solution with k≥2, then m>10^9.3·10⁶. This was the current best result and proved using a method due to L. Moser (1953). This approach cannot be improved to reach the benchmark m>10^10⁷. Here we achieve m>10^10⁹ by showing that 2k/(2m-3) is a convergent of log 2 and making an extensive continued fraction digits calculation of (log 2)/N, with N an appropriate integer. This method is very different from that of Moser. Indeed, our result seems to give one of very few instances where a large scale computation of a numerical constant has an application.
Subject: Erdős-Moser; equations; computations; integer solutions
Identifier: http://hdl.handle.net/1959.13/935003
Identifier: uon:11941
Identifier: ISSN:0025-5718
Rights: First published in Mathematics of Computation in 2011, published by the American Mathematical Society
Language: eng
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