Title: Three combinatorial applications



Abstract: This is not one seminar talk. This is three small seminars.  First, we prove a geometric result of Dirichlet using combinatorics. Second, as an application of posets we obtain Sylvester's two coin result.  Finally, we present a counting proof when 2 is a quadratic residue in a finite field.



The third topic is joint work with Frits Beukers and Karthik Chandrasekhar.