Further irreducibility criteria for polynomials with non-negative coefficients
Volume 175 / 2016
Acta Arithmetica 175 (2016), 137-181
MSC: Primary 11R09; Secondary 11C08, 12E05, 26C10.
DOI: 10.4064/aa8376-5-2016
Published online: 15 September 2016
Abstract
Let $f(x)$ be a polynomial with non-negative integer coefficients. This paper produces sharp bounds $M_{1}(b)$ depending on an integer $b \in [3,20]$ such that if each coefficient of $f(x)$ is $\le M_{1}(b)$ and $f(b)$ is prime, then $f(x)$ is irreducible. A number of other related results are obtained.
