The distribution of Bernoulli numbers modulo primes
type: Item
instance of: scholarly article
title: The distribution of Bernoulli numbers modulo primes
zbMATH Open document ID: 0644.10011
DOI: 10.1007/BF01194572
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: For an odd prime \(p\), let \(I\) by any set of \(m\) consecutive integers contained in \(\{1,\ldots,p-1\}\). The author proves the following result about Bernoulli numbers \(B\): for any rational integer \(\alpha\), the number of \(n\) in \(I\) such that \(\sum^{p-2}_{k=1}B_ kn^{p-1-k}\equiv \alpha \bmod p\), does not exceed \(4.5m^{2/3}\). A related statement about values of Bernoulli polynomials at \(1,\ldots,p-1\) is also proved. An application of the former result was contained in the author's paper [Q. J. Math., Oxf. II. Ser. 37, 257--261 (1986; Zbl 0604.10007)].
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 4049710
zbMATH Keywords: Kummer-Mirimanoff congruences, Fermat's problem
zbMATH Keywords: Bernoulli numbers
zbMATH Keywords: Bernoulli polynomials
author: Willem Louw Fouché
MaRDI profile type: Publication
cites work: ON THE KUMMER–MIRIMANOFF CONGRUENCES
cites work: Q3874309
cites work: Q3907638
cites work: Q5730963
cites work: Q3943047
full work available at URL: https://doi.org/10.1007/bf01194572
OpenAlex ID: W2101836493
description: scientific article; zbMATH DE number 4049710