A class of irreducible polynomials

Joshua Harrington; Lenny Jones

Colloquium Mathematicae, Tome 131 (2013), p. 113-119 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $f (x) = x ⁿ + k_{n - 1} x^{n - 1} + k_{n - 2} x^{n - 2} + \dots + k ₁ x + k ₀ \in ℤ [x]$ , where $3 \leq k_{n - 1} \leq k_{n - 2} \leq \dots \leq k ₁ \leq k ₀ \leq 2 k_{n - 1} - 3$ . 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.

Publié le : 2013-01-01

Zbl 06212153

EUDML-ID : urn:eudml:doc:283823

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-9,
     author = {Joshua Harrington and Lenny Jones},
     title = {A class of irreducible polynomials},
     journal = {Colloquium Mathematicae},
     volume = {131},
     year = {2013},
     pages = {113-119},
     zbl = {06212153},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-9}
}

Joshua Harrington; Lenny Jones. A class of irreducible polynomials. Colloquium Mathematicae, Tome 131 (2013) pp. 113-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-1-9/