JP Journal of Algebra, Number Theory and Applications
Volume 26, Issue 1, Pages 33 - 63
(August 2012)
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POLYNOMIALS WHOSE REDUCIBILITY IS RELATED TO THE GOLDBACH CONJECTURE
Peter Borwein, Kwok-Kwong Stephen Choi, Greg Martin and Charles L. Samuels
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Abstract: We introduce a collection of polynomials 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 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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