International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 19, Pages 3057-3073
doi:10.1155/IJMMS.2005.3057
Prime divisors of some shifted products
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.
Abstract
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(n−1) 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.