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

Florian Luca; Pieter Moree; Benne de Weger

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

Number Theory 2012-07-30 v1

Authors: Florian Luca , Pieter Moree , Benne de Weger

Abstract

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.

Keywords

diophantine equations cyclotomic polynomials finite group theory integer solutions

Cite

@article{arxiv.0907.5323,
  title  = {Some Diophantine equations from finite group theory: $\Phi_m(x)=2p^n-1$},
  author = {Florian Luca and Pieter Moree and Benne de Weger},
  journal= {arXiv preprint arXiv:0907.5323},
  year   = {2012}
}

Comments

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

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

Abstract

Keywords

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