Prime divisors of shifted factorials

Florian Luca; Igor E. Shparlinski

doi:10.1112/S0024609305004923

Prime divisors of shifted factorials

Florian Luca^*, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

17 Downloads (Pure)

Abstract

For any positive integer n we let P(n) be the largest prime factor of n. We improve and generalize several results of P. Erdos and C. Stewart on P(n!+1). In particular, we show that limsup_n→∞P(n!+1)/n ≥ 2.5, which improves their lower bound of limsup_n→∞P(n!+1)/n > 2.

Original language	English
Pages (from-to)	809-817
Number of pages	9
Journal	Bulletin of the London Mathematical Society
Volume	37
Issue number	6
DOIs	https://doi.org/10.1112/S0024609305004923
Publication status	Published - Dec 2005

Access to Document

10.1112/S0024609305004923

Publisher version (open access).pdfFinal published version, 221 KB

Cite this

@article{b00445de051f4d46937d4ffb7dbbd834,

title = "Prime divisors of shifted factorials",

abstract = "For any positive integer n we let P(n) be the largest prime factor of n. We improve and generalize several results of P. Erdos and C. Stewart on P(n!+1). In particular, we show that limsupn→∞P(n!+1)/n ≥ 2.5, which improves their lower bound of limsupn→∞P(n!+1)/n > 2.",

author = "Florian Luca and Shparlinski, {Igor E.}",

year = "2005",

month = dec,

doi = "10.1112/S0024609305004923",

language = "English",

volume = "37",

pages = "809--817",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "Wiley-Blackwell, Wiley",

number = "6",

}

TY - JOUR

T1 - Prime divisors of shifted factorials

AU - Luca, Florian

AU - Shparlinski, Igor E.

PY - 2005/12

Y1 - 2005/12

N2 - For any positive integer n we let P(n) be the largest prime factor of n. We improve and generalize several results of P. Erdos and C. Stewart on P(n!+1). In particular, we show that limsupn→∞P(n!+1)/n ≥ 2.5, which improves their lower bound of limsupn→∞P(n!+1)/n > 2.

AB - For any positive integer n we let P(n) be the largest prime factor of n. We improve and generalize several results of P. Erdos and C. Stewart on P(n!+1). In particular, we show that limsupn→∞P(n!+1)/n ≥ 2.5, which improves their lower bound of limsupn→∞P(n!+1)/n > 2.

UR - http://www.scopus.com/inward/record.url?scp=29144451835&partnerID=8YFLogxK

U2 - 10.1112/S0024609305004923

DO - 10.1112/S0024609305004923

M3 - Article

AN - SCOPUS:29144451835

VL - 37

SP - 809

EP - 817

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 6

ER -

Prime divisors of shifted factorials

Abstract

Access to Document

Other files and links

Fingerprint

Cite this