International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 19, Pages 3057-3073

Prime divisors of some shifted products

Eric Levieil,1 Florian Luca,1 and Igor E. Shparlinski1

1Département d'Informatique, École Normale Supérieure 45, rue d'Ulm, Paris Cedex 05 75230, France
2Instituto de Matemáticas, Universidad Nacional Autónoma de México, Morelia, Michoacán 58089, Mexico
3Department of Computing, Division of Information and Communication Sciences, Macquarie University, Sydney, NSW 2109, Australia

Received 12 May 2005; Revised 31 August 2005

Copyright © 2005 Eric Levieil et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study prime divisors of various sequences of positive integers A(n)+1, n=1,,N, such that the ratios a(n)=A(n)/A(n1) have some number-theoretic or combinatorial meaning. In the case a(n)=n, we obviously have A(n)=n!, for which several new results about prime divisors of n!+1 have recently been obtained.