  If $a>b$ and $n>1$ are positive integers and $a$ and $b$ are relatively prime
integers, then a large Zsigmondy prime for $(a,b,n)$ is a prime $p$ such that
$p \,|\, a^n-b^n$ but $p \,\nmid \, a^m-b^m$ for $1 \leq m < n$ and either $p^2
\, | \, a^n - b^n$ or $ p > n + 1$. We classify all the triples of integers
$(a, b, n)$ for which no large Zsigmondy prime exists.
