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

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

2009-07-30

arxiv.org/abs/0907.5323v1

Mathematics

Number Theory

17 pages, slightly extended version is available as Max-Planck preprint MPIM 2009-62

Scientific paper

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

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