Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu g**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: An Off-diagonal Version of a Theorem of Rado

Speaker: ** Aaron Robertson**, Colgate University

Date: Thursday, April 26, 2007 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

An equation is called r-regular if every r-coloring of the positive integers admits a monochromatic solution to the equation. Richard Rado completely categorized those equations that are r-regular for all r. A lesser known result of Rado's is that any 3 variable equation that has a solution in the positive integers is 2-regular. We present an off-diagonal version of this result as well as give the minimal n for certain equations for which every 2-coloring of [1,n] admits a monochromatic solution.