bibkey: moree2013moser authors: Pieter Moree year: 2013 title: Moser’s mathemagical work on the equation 1^k + 2^k + … + (m−1)^k = m^k doi: 10.1216/rmj-2013-43-5-1707 claim: “Theorem 2 (recording L. Moser, Scripta Math. 19 (1953) 84–88): if ∑_{i<m} i^k = m^k with m > 1, then for every prime p ∣ m−1: (p−1) ∣ k, p ∣ (m−1)/p + 1, p² ∤ m−1; hence m−1 is squarefree” strata_touched:
- D5/S3/PrimeForms/Obstructions/ErdosMoserLocalObstruction license: citation-only triage: anchor
Moser’s mathemagical work on the equation
Pieter Moree’s survey records Moser’s local congruence obstruction for a
solution of 1^k + 2^k + ... + (m - 1)^k = m^k. Theorem 2, explicitly
attributed there to L. Moser’s 1953 paper, states that every prime p dividing
m - 1 satisfies p - 1 | k and p | (m - 1) / p + 1; it also records that
m - 1 is squarefree. Thus p^2 does not divide m - 1.
This DOI-bearing secondary source attests the literature statement. It does not transfer Moree’s author, year, title, or DOI to Moser’s 1953 article. The repository’s Lean proof and its standalone block-decomposition and sum-transport statements are not attributed to either paper.
Search log
- 2026-09-05: Verified the article metadata as Pieter Moree, Moser’s
mathemagical work on the equation 1^k + 2^k + … + (m-1)^k = m^k, Rocky
Mountain Journal of Mathematics 43 (2013), no. 5, 1707-1737, DOI
10.1216/rmj-2013-43-5-1707. - 2026-09-05: Checked Theorem 2 and equations (5)-(7). They state the local
divisibility restrictions above, exclude repeated prime factors of
m - 1, and identify the proof as Moser’s 1953 argument. - 2026-09-05: Checked Moree’s bibliography entry [29], which records L. Moser, On the diophantine equation 1^n + 2^n + 3^n + … + (m - 1)^n = m^n, Scripta Math. 19 (1953), 84-88. Crossref, DataCite, OpenAlex, and Semantic Scholar yielded no DOI or arXiv identifier for that article, so this note uses Moree’s DOI and attributes only the recorded theorem to Moser.
Verified locator
- DOI: https://doi.org/10.1216/rmj-2013-43-5-1707
- Survey preprint: https://arxiv.org/abs/1011.2940
- Survey PDF: https://arxiv.org/pdf/1011.2940v2