Four Seemingly Unrelated Problems

Algebra Seminar
Friday, February 25, 2011 - 13:05
1 hour (actually 50 minutes)
Skiles 006
University of South Carolina
We begin this talk by discussing four different problems that arenumber theoretic or combinatorial in nature.  Two of these problems remainopen and the other two have known solutions.  We then explain how these seeminglyunrelated problems are connected to each other.  To disclose a little more information,one of the problems with a known solution is the following:  Is it possible to find anirrational number $q$ such that the infinite geometric sequence $1, q, q^{2}, \dots$has 4 terms in arithmetic progression?