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arXiv · 1408.4881

Polynomials whose reducibility is related to the Goldbach conjecture

Peter B. Borwein·Stephen K. K. Choi·Greg Martin·Charles L. Samuels
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Abstract

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.

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Peter B. Borwein, Stephen K. K. Choi, Greg Martin, Charles L. Samuels. 2014-08-21. Polynomials whose reducibility is related to the Goldbach conjecture. https://arxiv.org/abs/1408.4881

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