On the congruence \(1^m + 2^m + \ldots + m^m\equiv n \bmod m\) with \(n\mid m\)

DOI10.1007/s00605-014-0660-0zbMath1400.11007arXiv1309.7941OpenAlexW3123760299MaRDI QIDQ2354038

Jonathan Sondow, Antonio M. Oller-Marcén, José María Grau

Publication date: 10 July 2015

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.7941

zbMATH Keywords

asymptotic densitycongruencepower sumErdős-Moser equation

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Density, gaps, topology (11B05)

Related Items (4)

A Carlitz-von Staudt type theorem for finite rings ⋮ On \(\mu\)-Sondow numbers ⋮ Computing solutions to the congruence \(1^n + 2^n + \ldots + n^n \equiv p \pmod n\) ⋮ On power sums of matrices over a finite commutative ring

Uses Software

• OEIS

Cites Work

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• Moser's mathemagical work on the equation \(1^k+2^k+\ldots+(m-1)^k=m^k\)
• On the enumeration of finite groups
• Divisibility of power sums and the generalized Erdős-Moser equation
• Approximate formulas for some functions of prime numbers
• Reducing the Erdős–Moser Equation 1 n + 2 n + ⋯ + kn = (k + 1) n Modulo k and k 2
• A computational approach for solving $y^2=1^k+2^k+\dotsb+x^k$
• On the Diophantine equation $1^k+2^k+\dotsb+x^k=y^n$
• On the equation $\sum_{p|N}\frac1p+\frac1N = 1$, pseudoperfect numbers, and perfectly weighted graphs
• Sums of Powers of Integers
• Unsolved problems in number theory

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