Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T07:55:18.201Z Has data issue: false hasContentIssue false
  • English
  • Français

PRIME DIVISORS OF SHIFTED FACTORIALS

Published online by Cambridge University Press:  12 December 2005

FLORIAN LUCA  and
IGOR E. SHPARLINSKI
FLORIAN LUCA
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, CP 58089, Morelia, Michoacán, México, [email protected]
IGOR E. SHPARLINSKI
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia, [email protected]
Get access

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. Erdős and C. Stewart on $P(n!+1)$. In particular, we show that $\limsup_{n \to \infty}P(n!+1)/n \ge 2.5$, which improves their lower bound of $\limsup_{n \to \infty} P(n!+1)/n >2$.

Keywords

11A0511A0711J86
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 6 , December 2005 , pp. 809 - 817
Copyright
© The London Mathematical Society 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)