For given integers a,b, and j at least 1 we determine the set of integers n
for which a^n-b^n is divisible by n^j. For j=1,2, this set is usually infinite;
we find explicitly the exceptional cases for which a,b the set is finite. For
j=2, we use Zsigmondy's Theorem for this. For j at least 3 and gcd(a,b)=1, the
set is probably always finite; this seems difficult to prove, however.

We also show that determination of the set of integers n for which a^n+b^n is
divisible by n^j can be reduced to that of the above set.