Eric Levieil
Macquarie University
Title: On the Largest Prime Factor of n!+f(n) and generalizations
Abstract:
For any positive integer n, let P(n) be
the largest prime factor of n.
I will talk of some improvements and
generalizations of results of P.~Erdos and C.~Stewart on P(n!+1).
In particular, Florian Luca and Igor Shparlinski have proved that
$\limsup_{n \to \infty}P(n!+1)/n \ge 2.5$,
which improves the previous bound
$\limsup_{n \to \infty} P(n!+1)/n >2$.