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arXiv · 0907.5323

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

Florian Luca·Pieter Moree·Benne de Weger
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Abstract

We show that the equation in the title (with $Φ_m$ 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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Florian Luca, Pieter Moree, Benne de Weger. 2009-07-30. Some Diophantine equations from finite group theory: $Φ_m(x)=2p^n-1$. https://arxiv.org/abs/0907.5323

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