On the Nagell-Ljunggren equation (x^n - 1)/(x - 1) = y^q - Bugeaud, Yann; Mihailescu, Preda (MATHEMATICA SCANDINAVICA, 2007)
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.