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Number Theory Seminar

Presented by: Abdullah Al-Shaghay

Title: “Harrington Polynomials”

Abstract:

In a 2012 paper, J. Harrington investigated the factorization properties of polynomials of the form
f(x)=x^{n}+cx^{n-1}+cx^{n-2}+...+cx+c. In particular, it was asked:

1. For what positive integers n and nonzero integers c is f(x) irreducible?

2. If f(x) is reducible, then how does it factor?

We will discuss the results of Harrington's paper and talk about the idea of considering "Harrington polynomials with a gap size of a" for positive integers a: g(x)=x^{n}+cx^{n-a}+cx^{n-a-1}+cx^{n-a-2}+...+cx+c. 

 

Category

Lectures, Seminars

Time

Starts:
Ends:

Location

Seminar Room #227 Chase Building

Cost

Free

Contact

Ellen Lynch