Number Theory Seminar

“Irreducibility and Roots of a Class of Polynomials” presented by Abdullah Al-Shaghay, Dalhousie University


Additional Information

ABSTRACT: In a 2012 paper, J. Harrington investigated the factorization properties of polynomials of the form f(x) = x n + cxn−1 + cxn−2 + · · · + cx + c ∈ Z[x]. 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 + cxn−a + cxn−a−1 + cxn−a−2 + · · · + cx + c ∈ Z[x].


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