The greatest prime divisor of a product of terms in an arithmetic progression
type: Item
instance of: scholarly article
title: The greatest prime divisor of a product of terms in an arithmetic progression
zbMATH Open document ID: 1165.11014
DOI: 10.1016/S0019-3577(06)80042-X
author: Shanta Laishram
author: T. N. Shorey
published in: Indagationes Mathematicae. New Series
publication date: 2006-12-07T00:00:00Z
review text: The main result of this paper is the following: Theorem. Let \(d\) and \(k\) be rational integers \({}\geq 3\), then the greatest prime factor of the product \(n(n+d)\cdots (n+(k-1)d)\) is \({}>2k\), except for finitely many (explicitly given) exceptions. The proof is very delicate and contains the study of many subcases. The results used are also numerous and of a great variety.
Mathematics Subject Classification ID: 11B25
Mathematics Subject Classification ID: 11A41
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 5078186
zbMATH Keywords: greatest prime factor products of integers in arithmetic progressions
reviewed by: Maurice Mignotte
MaRDI profile type: Publication
cites work: A note on the Diophantine equation $a^x + b^y = c^z$
cites work: On a Theorem of Sylvester and Schur
cites work: The greatest prime divisor of a product of consecutive integers
cites work: Number of prime divisors in a product of consecutive integers
cites work: Number of prime divisors in a product of terms of an arithmetic progression
cites work: Q4149513
cites work: Primary cyclotomic units and a proof of Catalans conjecture
cites work: Insolvability of
cites work: Sur une classe d'équations exponentielles
cites work: Contributions towards a conjecture of Erdos on perfect powers in arithmetic progression
cites work: Some extensions and refinements of a theorem of Sylvester
cites work: Q3491636
cites work: Q3993308
full work available at URL: s0019-3577(06)80042-x
OpenAlex ID: W2036352952
description: scientific article; zbMATH DE number 5078186