On the Nagell-Ljunggren equation $(x^n - 1)/(x - 1) = y^q$

• Autores: Yann Bugeaud, Preda Mihailescu
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 101, Nº 2, 2007, págs. 177-183
• Idioma: inglés
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• Resumen

  • We establish several new results on the Nagell-Ljunggren equation $(x^n - 1)/(x-1) = y^q$. Among others, we prove that, for every solution $(x, y, n, q)$ to this equation, $n$ has at most four prime divisors, counted with their multiplicities.