2014/01/01 by Jonathan Sondow, Sondow, Jonathan, Emmanuel Tsukerman +1
Mathematics · #11B68 #11D61 #11D79 #11D88 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11B68 #msc:11D61 #msc:11D79 #msc:11D88
paper · pdf · doi:10.48550/arxiv.1401.0322
22 pages, comments are welcome
arxiv created 2014/01/01 · openalex publication_date 2014/01/01 · arxiv updated 2014/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Erdös-Moser equation is a Diophantine equation proposed more than 60 years ago which remains unresolved to this day. In this paper, we consider the problem in terms of divisibility of power sums and in terms of certain Egyptian fraction equations. As a consequence, we show that solutions must satisfy strong divisibility properties and a restrictive Egyptian fraction equation. Our studies lead us to results on the Bernoulli numbers and allow us to motivate Moser's original approach to the problem.