extremely unlikely that Fermat had a valid proof, most probably thought he did but was mistaken. I've messed around with the problem before, mostly trying modular representations and such
Landon Jones
i still hold faith that fermat was too based to make a mistake...
there has got to be a simple solution though... that shit seems too simple to require wiles tier math to solve it...
Brody Morris
Probably through the Triangle Inequality Theorem he found some sense of a geometric proof as an extension of Pythagoras' Theorem.
Josiah Anderson
it has a relatively simpler proof if you use the abc theorem
Christopher Collins
triangle inequality sounds like a good approach actually... I have played with expanding the nth root of the equation and seeing what headway I could make...