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

• Autores: Florian Luca, Pieter Moree, Benne de Weger
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 78, Fasc. 2, 2011, págs. 377-392
• Idioma: inglés
• DOI: 10.5486/pmd.2011.4771
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• Resumen

  • We show that the equation in the title (with m the mth cyclotomic polynomial) has no integer solution with n  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