{"paper":{"title":"The Erd\\H{o}s--Moser equation $1^k+2^k+...+(m-1)^k=m^k$ revisited using continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.NA"],"primary_cat":"math.NT","authors_text":"Australia), France), Germany), NSW, Pieter Moree (Bonn, Wadim Zudilin (Newcastle, Yves Gallot (Toulouse","submitted_at":"2009-07-08T08:26:19Z","abstract_excerpt":"If the equation of the title has an integer solution with $k\\ge2$, then $m>10^{9.3\\cdot10^6}$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1356","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}