Two Questions Concerning {0, 1}-polynomials
by
Carrie Finch
University of South Carolina
Coauthors: Michael Filaseta, Charles Nicol

Let S={k₁, k₂, ... } be an infinite set of positive integers. In this talk we discuss whether it is possible for S to have the property that for every nonempty subset {e₁, e₂, ..., e_n} of S, the polynomial 1+x^e₁ + ... + x^e_n is reducible. We then discuss whether it is possible for every nonempty subset of S to give rise to an irreducible polynomial. We show that the answer to the first question is no and the answer to the second question is yes.

Date received: March 16, 2005