h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

It's high time I get to the level you're at on this subject. I've taken some advanced number theory, and I have one of the intros to the Theorem and plenty of books on number theory, algebraic and otherwise; however, I'm in no position to handle this subject matter right now. Comments coming on 30 November--something to do other than physics for the next month, and then I've got to put my physics on a higher level than it is.

If nothing else, the article lists a treasure-trove of properties of the equation a**2-ab+b**2=T**3. Maybe it's just a coincidence that elliptic curves were used to prove FLT. About 12 years ago, I showed the proposition used to prove Wieferich's criterion to Hendrik Lenstra (an eminent mathematician somewhat involved with the proof of FLT). He said he thought the proposition could be proved using the norm-residue symbol (whatever that is) of class field theory. I've made some forays into algebraic number theory, but class field theory is way over my head. He didn't profess any more interest than that.