A beautiful and touching documentary about Fermat's last theorem, Wiles, and the other mathematicians involved in its proof: http://www.dailymotion.com/video/x223gx8
OTOH the history of mathematics seems to include the development of notation to hide complexity, so FLT can be written as A = sB
He had the proof for the power of 2, and when he wrote his line he might have had the proof for powers of 3 in mind (which he didnt write down) and thought that that one would generalize for all n. Which turned out to be true, but for completely different reasons.
See also https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem#Fermat...