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

Issue

Vol. 101 No. 2 (2007)

Section

Articles

How to Cite

[1]
Y. Bugeaud and P. Mihailescu, “On the Nagell-Ljunggren equation $(x^n - 1)/(x - 1) = y^q$”, Math. Scand., vol. 101, no. 2, pp. 177–183, Dec. 2007, doi: 10.7146/math.scand.a-15038.