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
Eric Levieil
, Florian Luca
and Igor E. Shparlinski
Département d'Informatique, École Normale Supérieure 45, rue d'Ulm, Paris Cedex 05 75230, France
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.