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

Yann Bugeaud; Preda Mihailescu

doi:10.7146/math.scand.a-15038

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

Authors

Yann Bugeaud
Preda Mihailescu

DOI:

https://doi.org/10.7146/math.scand.a-15038

Abstract

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.

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Published

2007-12-01

How to Cite

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