Zsigmondy’s theorem

For all positive integers $q>1$ and $n>1$, there exists a prime $p$ which divides $q^n-1$ but doesn’t divide $q^m-1$ for , except when $q=2^k-1$ and $n=2$ or $q=2$ and $n=6$.

Title	Zsigmondy’s theorem
Canonical name	ZsigmondysTheorem
Date of creation	2013-03-22 13:10:44
Last modified on	2013-03-22 13:10:44
Owner	lieven (1075)
Last modified by	lieven (1075)
Numerical id	6
Author	lieven (1075)
Entry type	Theorem
Classification	msc 11A51
Synonym	Birkhoff-Vandiver theorem