# 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 $0, except when $q=2^{k}-1$ and $n=2$ or $q=2$ and $n=6$.

Title Zsigmondy’s theorem ZsigmondysTheorem 2013-03-22 13:10:44 2013-03-22 13:10:44 lieven (1075) lieven (1075) 6 lieven (1075) Theorem msc 11A51 Birkhoff-Vandiver theorem