On a diophantine problem concerning Stirling numbers
type: Item
instance of: scholarly article
title: On a diophantine problem concerning Stirling numbers
zbMATH Open document ID: 0811.11017
DOI: 10.1007/BF01876037
published in: Acta Mathematica Hungarica
publication date: 1994-10-13T00:00:00Z
review text: The Stirling number of the second kind \(S_ k^ n\) is defined to be the number of partitions of the set \(\{1,\dots, n\}\) into \(k\) non-empty subsets. Let \(b>a>1\) be rational integers. Consider the equation \(S_ a^ x= S_ b^ y\) to be solved in integers \(x\), \(y\) with \(x>a\) and \(y>b\). In the note under review it is proved, using the theory of linear forms in logarithms, that all the solutions of the above equation satisfy \[ \max \{x,y\}< C b(\log b)^ 3 \log (b!/a!) \log a, \] where \(C\) is an effectively computable absolute constant.
reviewed by: Dimitros Poulakis
Mathematics Subject Classification ID: 11B73
Mathematics Subject Classification ID: 11D99
zbMATH DE Number: 638221
zbMATH Keywords: Stirling numbers
zbMATH Keywords: linear forms in logarithms
author: Ákos Pintér
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01876037
OpenAlex ID: W1991764073
description: scientific article; zbMATH DE number 638221