  We show that under the assumption of a 24-term version of Fermat's Last
Theorem, there exists an absolute constant c > 0 such that if S is a set of n >
n_0 positive integers satisfying |S.S| < n^(1+c), then the sumset S.S satisfies
|S+S| >> n^2. In other words, we prove a weak form of the Erdos-Szemeredi
sum-product conjecture, conditional on an extension of Fermat's Last Theorem.
Unconditionally, we prove this theorem for when S is a set of n monic
polynomials. We also prove an analogue of a theorem of Bourgain and Chang for
the ring C[x].
