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

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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.

2007-12-01

Bugeaud, Y., & Mihailescu, P. (2007). On the Nagell-Ljunggren equation

$(x^n - 1)/(x - 1) = y^q$ . MATHEMATICA SCANDINAVICA, 101(2), 177–183. https://doi.org/10.7146/math.scand.a-15038

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