#### Date of Award

1-1-2013

#### Document Type

Open Access Thesis

#### Department

Mathematics

#### First Advisor

Michael Filaseta

#### Abstract

Consider a polynomial f(x) having non-negative integer coefficients with f(b) prime for some integer b greater than or equal to 2. We will investigate the size of the coefficients of the polynomial and establish a largest such bound on the coefficients that would imply that f(x) is irreducible. A result of Filaseta and Gross has established sharp bounds on the coefficients of such a polynomial in the case that b = 10. We will expand these results for b in {8, 9, ..., 20}.

#### Recommended Citation

Cole, M.(2013). *Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients.* (Master's thesis). Retrieved from http://scholarcommons.sc.edu/etd/1590