On integers $n$ for which $X^n-1$ has a divisor of every degree
Acta Arithmetica, Tome 175 (2016) no. 3, pp. 225-243
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
A positive integer $n$ is called $\varphi$-practical if the polynomial $X^n-1$ has a divisor in $\mathbb Z[X]$ of every degree up to $n$. We show that the count of $\varphi$-practical numbers in $[1, x]$ is asymptotic to $C x/\!\log x$ for some positive constant $C$ as $x \rightarrow \infty$.
Keywords:
positive integer called varphi practical polynomial n has divisor mathbb every degree count varphi practical numbers asymptotic log positive constant rightarrow infty
Affiliations des auteurs :
Carl Pomerance 1 ; Lola Thompson 2 ; Andreas Weingartner 3
@article{10_4064_aa8354_6_2016,
author = {Carl Pomerance and Lola Thompson and Andreas Weingartner},
title = {On integers $n$ for which $X^n-1$ has a divisor of every degree},
journal = {Acta Arithmetica},
pages = {225--243},
publisher = {mathdoc},
volume = {175},
number = {3},
year = {2016},
doi = {10.4064/aa8354-6-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8354-6-2016/}
}
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Carl Pomerance; Lola Thompson; Andreas Weingartner. On integers $n$ for which $X^n-1$ has a divisor of every degree. Acta Arithmetica, Tome 175 (2016) no. 3, pp. 225-243. doi: 10.4064/aa8354-6-2016
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