%0 Journal Article
%T Polynomials whose reducibility is related to the Goldbach conjecture
%A Peter B. Borwein
%A Stephen K. K. Choi
%A Greg Martin
%A Charles L. Samuels
%J Mathematics
%D 2014
%I arXiv
%X We introduce a collection of polynomials $F_N$, associated to each positive integer $N$, whose divisibility properties yield a reformulation of the Goldbach conjecture. While this reformulation certainly does not lead to a resolution of the conjecture, it does suggest two natural generalizations for which we provide some numerical evidence. As these polynomials $F_N$ are independently interesting, we further explore their basic properties, giving, among other things, asymptotic estimates on the growth of their coefficients.
%U http://arxiv.org/abs/1408.4881v1