- 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>109.3·10⁶. 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>1010⁷. Here we achieve m>1010⁹ 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
- Full Text
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