Fermat's Last Theorem and Set Theory

It's well known (at least to mathematicians) that mathematics can be expressed using only the concepts of set theory. So… I was wondering how to express Fermat's Last Theorem using set theory. It shouldn't be that hard. After all, \(a^b\) is the cardinality of the set of possible functions with a domain of cardinality \(b\) and range inside a set of cardinality \(a\). Functions can be expressed in relations, which can be expressed in terms of sets of ordered pairs, which can be expressed in terms of set theory. Expanding all those definitions may get a bit complicated. I then remembered that I'm an expert on \(\mathrm{\TeX}\), which is based on expanding definitions. In other words, it should be relatively simple to express Fermat's Last Theorem using set theory in a \(\mathrm{\TeX}\) file.

As soon as I have something, I'll let you know.