On the equation \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\)
type: Item
instance of: scholarly article
title: On the equation \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\)
zbMATH Open document ID: 0757.11011
DOI: 10.1016/0019-3577(92)90029-K
author: N. Saradha
author: T. N. Shorey
published in: Indagationes Mathematicae. New Series
publication date: 1992-09-27T00:00:00Z
review text: In the second article [for the first one, ibid. 2, No. 4, 489-510 (1991) see the review above] the authors show that the equation \[ (x+1)\dots(x+k)=(y+1)\dots (y+mk) \] with integers \(x,y\geq 0\), \(k,m\geq 2\) implies that \(\max(x,y,k)\) is bounded by an effectively computable number depending only on \(m\). In an appendix by R. Balasubramanian, some relations, not necessary for the proof, of the implied polynomials are given.
Mathematics Subject Classification ID: 11D57
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 57234
zbMATH Keywords: products of consecutive integers
zbMATH Keywords: equal products
zbMATH Keywords: multiplicative diophantine equations
reviewed by: Bernd Richter
MaRDI profile type: Publication
cites work: On the irreducibility of certain polynomials
cites work: Q5621389
cites work: Q3859835
cites work: Q3283895
cites work: On the ratio of two blocks of consecutive integers
cites work: The equations \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\) with \(m=3,4\)
description: scientific article; zbMATH DE number 57234