### Four Seemingly Unrelated Problems

- Series
- Algebra Seminar
- Time
- Friday, February 25, 2011 - 13:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Michael Filaseta – University of South Carolina – filaseta@mailbox.sc.edu

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?