A number is called r-full if whenever a prime p divides it,
then so does pr. We discuss
the frequency of
solutions to the equation x + y = z
in r-full positive integers x, y, z,
relating it to work of Campana about
integral points on orbifolds. We present a
conjecture in the special case r = 2, together with some partial
results.
This is joint work with Karl Van Valckenborgh.