  The abc conjecture is one of the most famous unsolved problems in number
theory. The conjecture claims for each real $\epsilon > 0$ that there are only
a finite number of coprime positive integer solutions to the equation $a+b = c$
with $c > (rad(a b c))^{1+\epsilon}$. If true, the abc conjecture would imply
many other famous theorems and conjectures as corollaries. In this paper, we
discuss the abc conjecture and find new applications to powerful numbers, which
are integers $n$ for which $p^2 | n$ for every prime $p$ such that $p | n$. We
answer several questions from an earlier paper on this topic, assuming the
truth of the abc conjecture.
