On the equation \(x(x+d_ 1)\dots (x+(k-1)d_ 1)= y(y+d_ 2)\dots (y+(mk-1)d_ 2)\)
type: Item
instance of: scholarly article
title: On the equation \(x(x+d_ 1)\dots (x+(k-1)d_ 1)= y(y+d_ 2)\dots (y+(mk-1)d_ 2)\)
zbMATH Open document ID: 0798.11008
DOI: 10.1007/BF02830870
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1994-11-01T00:00:00Z
review text: For positive integers \(m \geq 2\), \(d_ 1\) and \(d_ 2\), the title equation is considered for unknown positive integers \(x,y\) and \(k \geq 2\). When \(d_ 1=d_ 2\) this equation reduces to the one investigated by the same authors in [Indag. Math. 3, 79-90 (1992; Zbl 0757.11011); ibid. 3, 237-242 (1992; Zbl 0763.11013)]. Here it is shown (and this extends previously obtained results) that the equation of the title implies that \(k\) is bounded, and for fixed \(k\) precise conditions are given under which the equation implies that both \(x\) and \(y\) are bounded by an effectively computable constant depending only on \(m\), \(d_ 1\), and \(d_ 2\).
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 562799
zbMATH Keywords: exponential diophantine equation
author: N. Saradha
author: T. N. Shorey
reviewed by: Roelof J. Stroeker
MaRDI profile type: Publication
cites work: On a Theorem of Sylvester and Schur
cites work: Approximate formulas for some functions of prime numbers
cites work: The equations \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\) with \(m=3,4\)
cites work: On the equation \((x+1)\dots(x+k)=(y+1)\dots(y+mk)\)
cites work: On the equation \(x(x +d) \cdots (x +(k - 1)d) = y(y + d) \cdots (y + (mk - 1)d)\)
full work available at URL: https://doi.org/10.1007/bf02830870
OpenAlex ID: W1995257686
description: scientific article; zbMATH DE number 562799