The criteria of Kummer and Mirimanoff extended to include 22 consecutive irregular pairs
type: Item
instance of: scholarly article
title: The criteria of Kummer and Mirimanoff extended to include 22 consecutive irregular pairs
zbMATH Open document ID: 0533.10009
author: Wilfrid Keller
author: Günter Löh
published in: Tokyo Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: If the Fermat equation \(x^ p+y^ p+z^ p=0\) (\(p\) an odd prime) has a solution with \(xyz\) prime to \(p\), then \(p\) divides the Bernoulli numbers \(B_{p-3},B_{p-5},\ldots,B_{p-19}\) [see \textit{H. Wada}, Tokyo J. Math. 3, 173--176 (1980; Zbl 0448.10016)]. The authors show by numerical computations that here 19 can be replaced by 45. Their method follows a program proposed by Wada [op. cit.]. The computations involve prime factorizations of certain integers having order of magnitude up to \(10^{60}\).
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11B68
Mathematics Subject Classification ID: 11-04
zbMATH DE Number: 3845659
zbMATH Keywords: Fermat last theorem
zbMATH Keywords: irregular prime
zbMATH Keywords: Bernoulli numbers
zbMATH Keywords: numerical computations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270213879
OpenAlex ID: W2058204361
DOI: 10.3836/TJM/1270213879
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description: scientific article; zbMATH DE number 3845659