1Department of Mathematics University of South Carolina Columbia, SC 29208, U.S.A. 2Department of Mathematics Shippensburg University Shippensburg, PA 17257, U.S.A.
Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 113-119
Let \[ f(x)=x^n+k_{n-1}x^{n-1}+k_{n-2}x^{n-2}+\cdots +k_1x+k_0\in \mathbb {Z}[x], \] where \[ 3\le k_{n-1}\le k_{n-2}\le \cdots \le k_1\le k_0\le 2k_{n-1}-3. \] We show that $f(x)$ and $f(x^2)$ are irreducible over $\mathbb {Q}$. Moreover, the upper bound of $2k_{n-1}-3$ on the coefficients of $f(x)$ is the best possible in this situation.
Keywords:
n n n n cdots mathbb where n n cdots n irreducible mathbb moreover upper bound n coefficients best possible situation
Affiliations des auteurs :
Joshua Harrington
1
;
Lenny Jones
2
1
Department of Mathematics University of South Carolina Columbia, SC 29208, U.S.A.
2
Department of Mathematics Shippensburg University Shippensburg, PA 17257, U.S.A.
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Joshua Harrington; Lenny Jones. A class of irreducible polynomials. Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 113-119. doi: 10.4064/cm132-1-9
