# A class of irreducible polynomials

Joshua Harrington; Lenny Jones

Colloquium Mathematicae (2013)

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

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topJoshua 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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