The equations \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\) with \(m=3,4\)
type: Item
instance of: scholarly article
title: The equations \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\) with \(m=3,4\)
zbMATH Open document ID: 0757.11010
DOI: 10.1016/0019-3577(91)90034-5
author: N. Saradha
author: T. N. Shorey
published in: Indagationes Mathematicae. New Series
publication date: 1992-09-27T00:00:00Z
review text: In the first article [for the second one, see ibid. 3, No. 1, 79-90 (1992; reviewed below)] the authors show that there are no solutions of the equation \[ (x+1)\dots (x+k)=(y+1)\dots (y+mk) \] for \(m=3\) and \(m=4\) with integers \(x,y\geq 0\), \(k\geq 2\). Extensive use is made of the symbolic computation program MATHEMATICA. In an appendix, Ph. Glesser gives some results, using the algebraic programming languge REDUCE.
Mathematics Subject Classification ID: 11D57
Mathematics Subject Classification ID: 11D41
zbMATH DE Number: 60871
zbMATH Keywords: products of consecutive integers
zbMATH Keywords: equal products
zbMATH Keywords: multiplicative diophantine equations
zbMATH Keywords: MATHEMATICA
zbMATH Keywords: REDUCE
reviewed by: Bernd Richter
describes a project that uses: REDUCE
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: 0019-3577(91)90034-5
OpenAlex ID: W1978430257
cites work: Q3859835
cites work: On the ratio of two blocks of consecutive integers
cites work: On the equation \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\)
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description: scientific article; zbMATH DE number 60871