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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, fluca@matmor.unam.mx
IGOR E. SHPARLINSKI
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia, igor@ics.mq.edu.au
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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

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