Some Diophantine equations from finite group theory: $\Phi_m (x) = 2p^n -1$

F. Luca; P. Moree; B.M.M. Weger, de

doi:10.5486/PMD.2011.4771

Some Diophantine equations from finite group theory: $\Phi_m (x) = 2p^n -1$

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We show that the equation in the title (with $\Psi_m$ the $m$th cyclotomic polynomial) has no integer solution with $n \geq 1$ in the cases (m,p) = (15,41), (15,5581), (10,271). These equations arise in a recent group theoretical investigation by Akhlaghi, Khosravi and Khatami.

Originele taal-2	Engels
Pagina's (van-tot)	377-392
Tijdschrift	Publicationes Mathematicae. Institutum Mathematicum Universitatis Debreceniensis
Volume	78
Nummer van het tijdschrift	2
DOI's	https://doi.org/10.5486/PMD.2011.4771
Status	Gepubliceerd - 2011

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10.5486/PMD.2011.4771

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title = "Some Diophantine equations from finite group theory: \$\textbackslash{}Phi\_m (x) = 2p\textasciicircum{}n -1\$",

abstract = "We show that the equation in the title (with \$\textbackslash{}Psi\_m\$ the \$m\$th cyclotomic polynomial) has no integer solution with \$n \textbackslash{}geq 1\$ in the cases (m,p) = (15,41), (15,5581), (10,271). These equations arise in a recent group theoretical investigation by Akhlaghi, Khosravi and Khatami.",

author = "F. Luca and P. Moree and \{Weger, de\}, B.M.M.",

year = "2011",

doi = "10.5486/PMD.2011.4771",

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journal = "Publicationes Mathematicae. Institutum Mathematicum Universitatis Debreceniensis",

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AU - Weger, de, B.M.M.

PY - 2011

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AB - We show that the equation in the title (with $\Psi_m$ the $m$th cyclotomic polynomial) has no integer solution with $n \geq 1$ in the cases (m,p) = (15,41), (15,5581), (10,271). These equations arise in a recent group theoretical investigation by Akhlaghi, Khosravi and Khatami.

U2 - 10.5486/PMD.2011.4771

DO - 10.5486/PMD.2011.4771

M3 - Article

SN - 0033-3883

VL - 78

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JO - Publicationes Mathematicae. Institutum Mathematicum Universitatis Debreceniensis

JF - Publicationes Mathematicae. Institutum Mathematicum Universitatis Debreceniensis

IS - 2

ER -

Some Diophantine equations from finite group theory: $\Phi_m (x) = 2p^n -1$

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