# A class of irreducible polynomials

Colloquium Mathematicae (2013)

• Volume: 132, Issue: 1, page 113-119
• ISSN: 0010-1354

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## Abstract

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Let $f\left(x\right)=xⁿ+{k}_{n-1}{x}^{n-1}+{k}_{n-2}{x}^{n-2}+\cdots +k₁x+k₀\in ℤ\left[x\right]$, where $3\le {k}_{n-1}\le {k}_{n-2}\le \cdots \le k₁\le k₀\le 2{k}_{n-1}-3$. We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of $2{k}_{n-1}-3$ on the coefficients of f(x) is the best possible in this situation.

## How to cite

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Joshua Harrington, and Lenny Jones. "A class of irreducible polynomials." Colloquium Mathematicae 132.1 (2013): 113-119. <http://eudml.org/doc/283823>.

@article{JoshuaHarrington2013,
abstract = {Let $f(x) = xⁿ + k_\{n-1\}x^\{n-1\} + k_\{n-2\}x^\{n-2\} + ⋯ +k₁x + k₀ ∈ ℤ[x]$, where $3 ≤ k_\{n-1\} ≤ k_\{n-2\} ≤ ⋯ ≤ k₁ ≤ k₀ ≤ 2k_\{n-1\} - 3$. We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of $2k_\{n-1\} - 3$ on the coefficients of f(x) is the best possible in this situation.},
author = {Joshua Harrington, Lenny Jones},
journal = {Colloquium Mathematicae},
keywords = {irreducible polynomial; Eneström-Kakeya},
language = {eng},
number = {1},
pages = {113-119},
title = {A class of irreducible polynomials},
url = {http://eudml.org/doc/283823},
volume = {132},
year = {2013},
}

TY - JOUR
AU - Joshua Harrington
AU - Lenny Jones
TI - A class of irreducible polynomials
JO - Colloquium Mathematicae
PY - 2013
VL - 132
IS - 1
SP - 113
EP - 119
AB - Let $f(x) = xⁿ + k_{n-1}x^{n-1} + k_{n-2}x^{n-2} + ⋯ +k₁x + k₀ ∈ ℤ[x]$, where $3 ≤ k_{n-1} ≤ k_{n-2} ≤ ⋯ ≤ k₁ ≤ k₀ ≤ 2k_{n-1} - 3$. We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of $2k_{n-1} - 3$ on the coefficients of f(x) is the best possible in this situation.
LA - eng
KW - irreducible polynomial; Eneström-Kakeya
UR - http://eudml.org/doc/283823
ER -

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