There is a long tradition of mathematicians remarking that FLT in itself is a rather isolated claim, attractive only because of its simplicity. And people often note a great thing about current proofs of FLT is their use of the modularity thesis which is just the opposite: arcane, and richly connected to a lot of results.
But have there been uses of FLT itself? Beyond implying simple variants of itself, are there any more serious uses yet?
I notice the discussion in Fermat's Last Theorem and Computability Theory concludes that one purported use is not seriously using FLT.