Consecutive powers
type: Item
instance of: scholarly article
title: Consecutive powers
zbMATH Open document ID: 0537.10009
published in: Expositiones Mathematicae
publication date: 1984-01-01T00:00:00Z
review text: The author gives a very readable history of Catalan's problem. He begins with Levy ben Gerson's solution of Philippe de Vitry's question: Can \(3^ m\pm 1\) be a power of 2 ? The article ends with the announcement of an unpublished result of R. Tijdeman: For a natural number N let S be the set of numbers, all of whose prime factors are less than N. Then there exists a computable constant C, depending only on N, such that if m,n,x,\(y\geq 2\), \(\gcd(ax,k)=1,\quad | a|,\quad | b|,\quad | k| \in S,\) and \(ax^ m-by^ n=k\) then \(\max \{| a|,| b|,| k|,m,n,x,y\}\leq C.\)
Mathematics Subject Classification ID: 11D41
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 01A35
Mathematics Subject Classification ID: 01A60
zbMATH DE Number: 3853180
zbMATH Keywords: consecutive powers
zbMATH Keywords: sequence of squares and cubes
zbMATH Keywords: history of Catalan problem
zbMATH Keywords: bibliography
author: Paulo Ribenboim
reviewed by: Bernd Richter
MaRDI profile type: Publication
Recommended article: Consecutive powers in continued fractions
Recommended article: POWERS FROM PRODUCTS OF CONSECUTIVE TERMS IN ARITHMETIC PROGRESSION
Recommended article: Powers in arithmetic progressions
Recommended article: On powers that are sums of consecutive like powers
Recommended article: Almost perfect powers in consecutive integers
Recommended article: On the Sum of Powers of Consecutive Integers
Recommended article: Power values of sums of products of consecutive integers
Recommended article: Arithmetic progressions consisting of unlike powers
Recommended article: Q3613983
Recommended article: Powers of sequences and recurrence
description: scientific article; zbMATH DE number 3853180