Geodesic
On integers $n$ for which $X^n-1$ has a divisor of every degree
Carl Pomerance 1   ; Lola Thompson 2   ; Andreas Weingartner 3
1 Department of Mathematics Dartmouth College Hanover, NH 03755, U.S.A.
2 Department of Mathematics Oberlin College Oberlin, OH 44074, U.S.A.
3 Department of Mathematics Southern Utah University Cedar City, UT 84720, U.S.A.
Acta Arithmetica, Tome 175 (2016) no. 3, pp. 225-243 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $x \rightarrow \infty$.
DOI : 10.4064/aa8354-6-2016
Keywords: positive integer called varphi practical polynomial n has divisor mathbb every degree count varphi practical numbers asymptotic log positive constant rightarrow infty

Carl Pomerance  1   ; Lola Thompson  2   ; Andreas Weingartner  3

1 Department of Mathematics Dartmouth College Hanover, NH 03755, U.S.A.
2 Department of Mathematics Oberlin College Oberlin, OH 44074, U.S.A.
3 Department of Mathematics Southern Utah University Cedar City, UT 84720, U.S.A. 
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     title = {On integers $n$ for which $X^n-1$ has a divisor of every degree},
     journal = {Acta Arithmetica},
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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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