TY - JOUR
T1 - Some Diophantine equations from finite group theory: $\Phi_m (x) = 2p^n -1$
AU - Luca, F.
AU - Moree, P.
AU - Weger, de, B.M.M.
PY - 2011
Y1 - 2011
N2 - 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.
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
SP - 377
EP - 392
JO - Publicationes Mathematicae. Institutum Mathematicum Universitatis Debreceniensis
JF - Publicationes Mathematicae. Institutum Mathematicum Universitatis Debreceniensis
IS - 2
ER -