The factorization of $f(x)x^n+g(x)$ with $f(x)$ monic and of degree $\le 2$.

Harrington, Joshua; Vincent, Andrew; White, Daniel

doi:10.5802/jtnb.849

The factorization of

f (x) x^{n} + g (x)

with

f (x)

monic and of degree

\leq 2

Harrington, Joshua ¹; Vincent, Andrew ²; White, Daniel ¹

¹ Department of Mathematics University of South Carolina Columbia, SC 29208
² Department of Mathematics University of South Carolina Columbia, SC, 29208

Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 3, pp. 565-578.

Abstract
Résumé

In this paper we investigate the factorization of the polynomials $f (x) x^{n} + g (x) \in ℤ [x]$ in the special case where $f (x)$ is a monic quadratic polynomial with negative discriminant. We also mention similar results in the case that $f (x)$ is monic and linear.

Dans cet article, nous étudions la factorisation des polynômes $f (x) x^{n} + g (x) \in ℤ [x]$ dans le cas particulier où $f (x)$ est un polynôme quadratique unitaire avec discriminant négatif. Nous mentionnons également des résultats similaires dans le cas où $f (x)$ est unitaire et linéaire.

MR Zbl

DOI: 10.5802/jtnb.849

Classification: 11C08, 12E05, 26C10
Mots-clés : polynomials, trinomials, irreducible, factorization

Author's affiliations:

Harrington, Joshua ¹; Vincent, Andrew ²; White, Daniel ¹

¹ Department of Mathematics University of South Carolina Columbia, SC 29208
² Department of Mathematics University of South Carolina Columbia, SC, 29208

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     title = {The factorization of $f(x)x^n+g(x)$ with $f(x)$ monic and of degree $\le 2$.},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {565--578},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
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     zbl = {1293.11049},
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     url = {https://www.numdam.org/articles/10.5802/jtnb.849/}
}

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Harrington, Joshua; Vincent, Andrew; White, Daniel. The factorization of $f(x)x^n+g(x)$ with $f(x)$ monic and of degree $\le 2$.. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 3, pp. 565-578. doi : 10.5802/jtnb.849. https://www.numdam.org/articles/10.5802/jtnb.849/

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