**Date & Time:** Thursday, August 13, 2015, 15:30-16:30.

**Venue:** Ramanujan Hall

**Title:** The product of two or more factorials being a factorial

**Speaker:** Saranya Nair, IIT Bombay

**Abstract:** A well-known theorem of Sylvester for consecutive integers
states that the product of $k$ consecutive integers $m,m+1,...,m+k-1$ is
divisible by a prime greater than $k$ if $m >k.$ We discuss an improvement
of this result with it's application to a Diophantine equation considered
by Erdos, product of two or more factorials being a factorial. Further we
give an other application to irreducibility of Laguerre polynomials
including truncated exponential polynomials.