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- W2968155797 abstract "If the equation of the title has an integer solution with $kge2$, then $m>10^{9.3cdot10^6}$. 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 $m>10^{10^7}$. Here we achieve $m>10^{10^9}$ by showing that $2k/(2m-3)$ is a convergent of $log2$ and making an extensive continued fraction digits calculation of $(log2)/N$, 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." @default.
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- W2968155797 date "2011-05-01" @default.
- W2968155797 modified "2023-10-16" @default.
- W2968155797 title "The Erdős–Moser equation $1^{k}+2^{k}+dots+(m-1)^{k}=m^{k}$ revisited using continued fractions" @default.
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- W2968155797 doi "https://doi.org/10.1090/s0025-5718-2010-02439-1" @default.
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