Reducing the Erdős–Moser Equation 1 n + 2 n + ⋯ + kn = (k + 1) n Modulo k and k 2

DOI10.1515/INTEG.2011.058zbMath1233.11038arXiv1011.2154OpenAlexW2963115705MaRDI QIDQ3108534

Jonathan Sondow, Kieren MacMillan

Publication date: 4 January 2012

Published in: Integers (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.2154

zbMATH Keywords

congruenceFermat quotientsupercongruencepseudoperfect numberLerch's formulaWilson quotientEisenstein's relationErdös-Moser equaton

Mathematics Subject Classification ID

Congruences in many variables (11D79) Exponential Diophantine equations (11D61) Primes (11A41)

Related Items (6)

Primary Pseudoperfect Numbers, Arithmetic Progressions, and the Erdős-Moser Equation ⋮ Moser's mathemagical work on the equation \(1^k+2^k+\ldots+(m-1)^k=m^k\) ⋮ A von Staudt-type result for \(\sum _{z\in \mathbb {Z}_n[i} z^k\)] ⋮ Preface: CALDAM 2017 ⋮ Computing solutions to the congruence \(1^n + 2^n + \ldots + n^n \equiv p \pmod n\) ⋮ On the congruence \(1^m + 2^m + \ldots + m^m\equiv n \bmod m\) with \(n\mid m\)

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