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

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.