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

9 Citations (Scopus)

57 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

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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.",

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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 - https://www.scopus.com/pages/publications/29144451835

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DO - 10.1112/S0024609305004923

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JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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Prime divisors of shifted factorials

Abstract

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