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

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

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)377-392
JournalPublicationes Mathematicae. Institutum Mathematicum Universitatis Debreceniensis
Volume78
Issue number2
DOIs
Publication statusPublished - 2011

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